SPRECT_1

:: SPRECT_1 semantic presentation

REAL is non empty V32() V199() V200() V201() V205() non bounded_below non bounded_above V245() set
NAT is V199() V200() V201() V202() V203() V204() V205() bounded_below Element of bool REAL
bool REAL is non empty set
COMPLEX is non empty V32() V199() V205() set
omega is V199() V200() V201() V202() V203() V204() V205() bounded_below set
bool omega is non empty set
bool NAT is non empty set
1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
[:1,1:] is non empty V23( RAT ) V23( INT ) V189() V190() V191() V192() set
RAT is non empty V32() V199() V200() V201() V202() V205() set
INT is non empty V32() V199() V200() V201() V202() V203() V205() set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty V23( RAT ) V23( INT ) V189() V190() V191() V192() set
bool [:[:1,1:],1:] is non empty set
[:[:1,1:],REAL:] is non empty V189() V190() V191() set
bool [:[:1,1:],REAL:] is non empty set
[:REAL,REAL:] is non empty V189() V190() V191() set
[:[:REAL,REAL:],REAL:] is non empty V189() V190() V191() set
bool [:[:REAL,REAL:],REAL:] is non empty set
[:2,2:] is non empty V23( RAT ) V23( INT ) V189() V190() V191() V192() set
[:[:2,2:],REAL:] is non empty V189() V190() V191() set
bool [:[:2,2:],REAL:] is non empty set
bool [:REAL,REAL:] is non empty set
TOP-REAL 2 is non empty TopSpace-like V114() V145() V146() V147() V148() V149() V150() V151() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
K257( the carrier of (TOP-REAL 2)) is non empty functional FinSequence-membered M15( the carrier of (TOP-REAL 2))
bool the carrier of (TOP-REAL 2) is non empty set
[: the carrier of (TOP-REAL 2),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of (TOP-REAL 2),REAL:] is non empty set
[:COMPLEX,COMPLEX:] is non empty V189() set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is non empty V189() V190() V191() set
bool [:COMPLEX,REAL:] is non empty set
ExtREAL is non empty V200() V245() set
{} is empty trivial Function-like functional FinSequence-membered V199() V200() V201() V202() V203() V204() V205() bounded_below V245() set
the empty trivial Function-like functional FinSequence-membered V199() V200() V201() V202() V203() V204() V205() bounded_below V245() set is empty trivial Function-like functional FinSequence-membered V199() V200() V201() V202() V203() V204() V205() bounded_below V245() set
3 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
Seg 1 is non empty V32() 1 -element V199() V200() V201() V202() V203() V204() left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
{1} is non empty trivial V199() V200() V201() V202() V203() V204() left_end bounded_below set
Seg 2 is non empty V32() 2 -element V199() V200() V201() V202() V203() V204() left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
{1,2} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
proj1 is V19() V22( the carrier of (TOP-REAL 2)) V23( REAL ) Function-like V44( the carrier of (TOP-REAL 2), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 is V19() V22( the carrier of (TOP-REAL 2)) V23( REAL ) Function-like V44( the carrier of (TOP-REAL 2), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of (TOP-REAL 2),REAL:]
[:(Seg 2),(Seg 2):] is non empty V23( RAT ) V23( INT ) V189() V190() V191() V192() set
[1,1] is non empty set
{1,1} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{1,1},{1}} is non empty set
[1,2] is non empty set
{{1,2},{1}} is non empty set
[2,1] is non empty set
{2,1} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{2} is non empty trivial V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{2,1},{2}} is non empty set
[2,2] is non empty set
{2,2} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{2,2},{2}} is non empty set
0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V97() V188() V199() V200() V201() V202() V203() V204() V205() bounded_below V245() Element of NAT
4 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
5 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
<*0*> is non empty trivial V19() V22( NAT ) V23( REAL ) Function-like one-to-one constant V32() 1 -element FinSequence-like FinSubsequence-like V189() V190() V191() increasing V194() V195() V196() M16( REAL ,K258(1,REAL))
K258(1,REAL) is functional FinSequence-membered M15( REAL )
f is V19() V22( NAT ) Function-like V32() FinSequence-like FinSubsequence-like set
A1 is V19() V22( NAT ) Function-like V32() FinSequence-like FinSubsequence-like set
f ^ A1 is V19() V22( NAT ) Function-like V32() FinSequence-like FinSubsequence-like set
rng f is set
A2 is V19() V22( NAT ) Function-like constant V32() FinSequence-like FinSubsequence-like set
rng A2 is trivial set
rng A1 is set
f is set
A1 is set
<*f,A1*> is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like set
rng <*f,A1*> is set
<*f*> is non empty trivial V19() V22( NAT ) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like set
<*A1*> is non empty trivial V19() V22( NAT ) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like set
<*f*> ^ <*A1*> is non empty V19() V22( NAT ) Function-like V32() 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
rng (<*f*> ^ <*A1*>) is set
rng <*f*> is trivial set
rng <*A1*> is trivial set
(rng <*f*>) \/ (rng <*A1*>) is set
{A1} is non empty trivial set
(rng <*f*>) \/ {A1} is non empty set
{f} is non empty trivial set
{f} \/ {A1} is non empty set
{f,A1} is non empty set
A2 is V19() Function-like constant set
rng A2 is trivial set
f is set
A1 is set
A2 is set
<*f,A1,A2*> is non empty non trivial V19() V22( NAT ) Function-like V32() 3 -element FinSequence-like FinSubsequence-like set
rng <*f,A1,A2*> is set
<*f*> is non empty trivial V19() V22( NAT ) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like set
<*A1*> is non empty trivial V19() V22( NAT ) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like set
<*f*> ^ <*A1*> is non empty V19() V22( NAT ) Function-like V32() 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
<*A2*> is non empty trivial V19() V22( NAT ) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like set
(<*f*> ^ <*A1*>) ^ <*A2*> is non empty V19() V22( NAT ) Function-like V32() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
rng ((<*f*> ^ <*A1*>) ^ <*A2*>) is set
rng (<*f*> ^ <*A1*>) is set
rng <*A2*> is trivial set
(rng (<*f*> ^ <*A1*>)) \/ (rng <*A2*>) is set
{A2} is non empty trivial set
(rng (<*f*> ^ <*A1*>)) \/ {A2} is non empty set
rng <*f*> is trivial set
rng <*A1*> is trivial set
(rng <*f*>) \/ (rng <*A1*>) is set
((rng <*f*>) \/ (rng <*A1*>)) \/ {A2} is non empty set
{A1} is non empty trivial set
(rng <*f*>) \/ {A1} is non empty set
((rng <*f*>) \/ {A1}) \/ {A2} is non empty set
{f} is non empty trivial set
{f} \/ {A1} is non empty set
({f} \/ {A1}) \/ {A2} is non empty set
{f,A1} is non empty set
{f,A1} \/ {A2} is non empty set
{f,A1,A2} is non empty set
a1 is V19() Function-like constant set
rng a1 is trivial set
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
bool the carrier of f is non empty set
A1 is Element of bool the carrier of f
A2 is non empty Element of bool the carrier of f
f | A2 is non empty strict TopSpace-like SubSpace of f
the carrier of (f | A2) is non empty set
bool the carrier of (f | A2) is non empty set
a1 is Element of bool the carrier of (f | A2)
{} (f | A2) is empty trivial proper Function-like functional FinSequence-membered closed compact V199() V200() V201() V202() V203() V204() V205() bounded_below V245() Element of bool the carrier of (f | A2)
f is TopStruct
the carrier of f is set
bool the carrier of f is non empty set
A2 is Element of bool the carrier of f
A1 is Element of bool the carrier of f
f | A2 is strict SubSpace of f
the carrier of (f | A2) is set
bool the carrier of (f | A2) is non empty set
a1 is Element of bool the carrier of (f | A2)
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
bool the carrier of f is non empty set
A1 is non empty Element of bool the carrier of f
A2 is Element of bool the carrier of f
a1 is Element of bool the carrier of f
a2 is Element of bool the carrier of f
A2 \/ a1 is Element of bool the carrier of f
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
bool the carrier of f is non empty set
A1 is non empty Element of bool the carrier of f
A2 is Element of bool the carrier of f
a1 is Element of bool the carrier of f
a2 is Element of bool the carrier of f
c₆ is Element of bool the carrier of f
A2 \/ a1 is Element of bool the carrier of f
a2 \/ c₆ is Element of bool the carrier of f
{A2,a1} is non empty set
{a2,c₆} is non empty set
A2 is set
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*f,A1,A2*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*f,A1,A2*> is Element of bool the carrier of (TOP-REAL 2)
len <*f,A1,A2*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (<*f,A1,A2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*f,A1,A2*> ) } is set
union { (LSeg (<*f,A1,A2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*f,A1,A2*> ) } is set
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (A1,A2) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * A1) + (b₁ * A2)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,A1)) \/ (LSeg (A1,A2)) is non empty Element of bool the carrier of (TOP-REAL 2)
<*f,A1*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*f,A1*> /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*A2*> is non empty trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like special M16( the carrier of (TOP-REAL 2),K258(1, the carrier of (TOP-REAL 2)))
K258(1, the carrier of (TOP-REAL 2)) is functional FinSequence-membered M15( the carrier of (TOP-REAL 2))
<*A2*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*f,A1*> ^ <*A2*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len <*f,A1*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
L~ <*f,A1*> is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*f,A1*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*f,A1*> ) } is set
union { (LSeg (<*f,A1*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*f,A1*> ) } is set
(L~ <*f,A1*>) \/ (LSeg (A1,A2)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ <*A2*> is Element of bool the carrier of (TOP-REAL 2)
len <*A2*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (<*A2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*A2*> ) } is set
union { (LSeg (<*A2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*A2*> ) } is set
((L~ <*f,A1*>) \/ (LSeg (A1,A2))) \/ (L~ <*A2*>) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ <*f,A1*>) \/ (LSeg (A1,A2))) \/ {} is non empty set
f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
TOP-REAL f is non empty TopSpace-like V114() V145() V146() V147() V148() V149() V150() V151() strict RLTopStruct
the carrier of (TOP-REAL f) is non empty set
A1 is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL f)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL f)
L~ A1 is Element of bool the carrier of (TOP-REAL f)
bool the carrier of (TOP-REAL f) is non empty set
len A1 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (A1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A1 ) } is set
union { (LSeg (A1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A1 ) } is set
f is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
A1 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
A1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
A2 is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len A2 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
L~ A2 is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (A2,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A2 ) } is set
union { (LSeg (A2,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A2 ) } is set
a1 is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
a2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*a2*> is non empty trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like constant V32() 1 -element FinSequence-like FinSubsequence-like special M16( the carrier of (TOP-REAL 2),K258(1, the carrier of (TOP-REAL 2)))
K258(1, the carrier of (TOP-REAL 2)) is functional FinSequence-membered M15( the carrier of (TOP-REAL 2))
a1 ^ <*a2*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len a1 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len <*a2*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len a1) + (len <*a2*>) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len a1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
L~ a1 is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (a1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len a1 ) } is set
union { (LSeg (a1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len a1 ) } is set
L~ <*a2*> is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*a2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*a2*> ) } is set
union { (LSeg (<*a2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*a2*> ) } is set
{} (TOP-REAL 2) is empty trivial proper Function-like functional FinSequence-membered closed compact V199() V200() V201() V202() V203() V204() V205() V211( TOP-REAL 2) circled bounded_below V245() Element of bool the carrier of (TOP-REAL 2)
a1 /. (len a1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*a2*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
LSeg ((a1 /. (len a1)),(<*a2*> /. 1)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (a1 /. (len a1))) + (b₁ * (<*a2*> /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ a1) \/ (LSeg ((a1 /. (len a1)),(<*a2*> /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ <*a2*> is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*a2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*a2*> ) } is set
union { (LSeg (<*a2*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*a2*> ) } is set
((L~ a1) \/ (LSeg ((a1 /. (len a1)),(<*a2*> /. 1)))) \/ (L~ <*a2*>) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ a1) \/ (LSeg ((a1 /. (len a1)),(<*a2*> /. 1)))) \/ {} is non empty set
A1 is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len A1 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
L~ A1 is Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (A1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A1 ) } is set
union { (LSeg (A1,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len A1 ) } is set
{} (TOP-REAL 2) is empty trivial proper Function-like functional FinSequence-membered closed compact V199() V200() V201() V202() V203() V204() V205() V211( TOP-REAL 2) circled bounded_below V245() Element of bool the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
A1 is Element of bool the carrier of (TOP-REAL 2)
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `2 is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
A1 is Element of bool the carrier of (TOP-REAL 2)
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
R^2-unit_square is non empty non trivial compact special_polygonal Element of bool the carrier of (TOP-REAL 2)
|[0,0]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
|[0,1]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,0]|,|[0,1]|) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,0]|) + (b₁ * |[0,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
|[1,1]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,1]|,|[1,1]|) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,1]|) + (b₁ * |[1,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[1,0]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,|[1,0]|) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,1]|) + (b₁ * |[1,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,0]|,|[0,0]|) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[0,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
|[0,1]| `2 is V11() real ext-real Element of REAL
|[0,0]| `2 is V11() real ext-real Element of REAL
|[1,1]| `1 is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
N-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (N-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (N-most f))) V267( the carrier of ((TOP-REAL 2) | (N-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (N-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty set
lower_bound (proj1 | (N-most f)) is V11() real ext-real Element of REAL
(proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most f))),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
N-max f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most f))),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
S-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(SE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (S-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (S-most f))) V267( the carrier of ((TOP-REAL 2) | (S-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (S-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:] is non empty set
lower_bound (proj1 | (S-most f)) is V11() real ext-real Element of REAL
(proj1 | (S-most f)) .: the carrier of ((TOP-REAL 2) | (S-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (S-most f)) .: the carrier of ((TOP-REAL 2) | (S-most f))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most f))),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
S-max f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (S-most f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (S-most f)) .: the carrier of ((TOP-REAL 2) | (S-most f))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most f))),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
W-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
W-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (W-most f))) V267( the carrier of ((TOP-REAL 2) | (W-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty set
lower_bound (proj2 | (W-most f)) is V11() real ext-real Element of REAL
(proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f))) is V11() real ext-real Element of REAL
|[(W-bound f),(lower_bound (proj2 | (W-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
W-max f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most f)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f))) is V11() real ext-real Element of REAL
|[(W-bound f),(upper_bound (proj2 | (W-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
E-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
E-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(NE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (E-most f))) V267( the carrier of ((TOP-REAL 2) | (E-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:] is non empty set
lower_bound (proj2 | (E-most f)) is V11() real ext-real Element of REAL
(proj2 | (E-most f)) .: the carrier of ((TOP-REAL 2) | (E-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (E-most f)) .: the carrier of ((TOP-REAL 2) | (E-most f))) is V11() real ext-real Element of REAL
|[(E-bound f),(lower_bound (proj2 | (E-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
E-max f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most f)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (E-most f)) .: the carrier of ((TOP-REAL 2) | (E-most f))) is V11() real ext-real Element of REAL
|[(E-bound f),(upper_bound (proj2 | (E-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
E-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(NE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (E-most f))) V267( the carrier of ((TOP-REAL 2) | (E-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most f)),REAL:] is non empty set
lower_bound (proj2 | (E-most f)) is V11() real ext-real Element of REAL
(proj2 | (E-most f)) .: the carrier of ((TOP-REAL 2) | (E-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (E-most f)) .: the carrier of ((TOP-REAL 2) | (E-most f))) is V11() real ext-real Element of REAL
|[(E-bound f),(lower_bound (proj2 | (E-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
W-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (W-most f))) V267( the carrier of ((TOP-REAL 2) | (W-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty set
lower_bound (proj2 | (W-most f)) is V11() real ext-real Element of REAL
(proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f))) is V11() real ext-real Element of REAL
|[(W-bound f),(lower_bound (proj2 | (W-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
(W-min f) `1 is V11() real ext-real Element of REAL
(E-min f) `1 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `1 is V11() real ext-real Element of REAL
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (N-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (N-most f))) V267( the carrier of ((TOP-REAL 2) | (N-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (N-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty set
lower_bound (proj1 | (N-most f)) is V11() real ext-real Element of REAL
(proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most f))),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
S-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(SE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (S-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (S-most f))) V267( the carrier of ((TOP-REAL 2) | (S-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (S-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most f)),REAL:] is non empty set
lower_bound (proj1 | (S-most f)) is V11() real ext-real Element of REAL
(proj1 | (S-most f)) .: the carrier of ((TOP-REAL 2) | (S-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (S-most f)) .: the carrier of ((TOP-REAL 2) | (S-most f))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most f))),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
(S-min f) `2 is V11() real ext-real Element of REAL
(N-min f) `2 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `2 is V11() real ext-real Element of REAL
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (N-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (N-most f))) V267( the carrier of ((TOP-REAL 2) | (N-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (N-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most f)),REAL:] is non empty set
lower_bound (proj1 | (N-most f)) is V11() real ext-real Element of REAL
(proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (N-most f)) .: the carrier of ((TOP-REAL 2) | (N-most f))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most f))),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
(N-min f) `1 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
W-min f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
W-most f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ f is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most f) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (W-most f))) V267( the carrier of ((TOP-REAL 2) | (W-most f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most f)),REAL:] is non empty set
lower_bound (proj2 | (W-most f)) is V11() real ext-real Element of REAL
(proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (W-most f)) .: the carrier of ((TOP-REAL 2) | (W-most f))) is V11() real ext-real Element of REAL
|[(W-bound f),(lower_bound (proj2 | (W-most f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
(W-min f) `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = E-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
(SE-corner f) `1 is V11() real ext-real Element of REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = S-bound f ) } is set
(SW-corner f) `1 is V11() real ext-real Element of REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
(SE-corner f) `1 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `2 is V11() real ext-real Element of REAL
c₆ `1 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = N-bound f ) } is set
(NW-corner f) `1 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `2 is V11() real ext-real Element of REAL
c₆ `1 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = W-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
(SW-corner f) `1 is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
(NW-corner f) `1 is V11() real ext-real Element of REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
a2 is set
c₆ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ `1 is V11() real ext-real Element of REAL
c₆ `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ (LSeg ((NW-corner f),(NE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
{(NW-corner f)} is non empty trivial set
A1 is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = N-bound f ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = W-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) /\ (LSeg ((NE-corner f),(SE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
{(NE-corner f)} is non empty trivial set
A1 is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = E-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = N-bound f ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(NE-corner f))) /\ (LSeg ((SW-corner f),(SE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
{(SE-corner f)} is non empty trivial set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NE-corner f),(SE-corner f))) /\ (LSeg ((SE-corner f),(SW-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
A1 is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = S-bound f ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = E-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(SW-corner f))) /\ (LSeg ((SW-corner f),(SE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
{(SW-corner f)} is non empty trivial set
A1 is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = S-bound f ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = W-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is non empty compact non vertical Element of bool the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
W-bound f is V11() real ext-real Element of REAL
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
f is non empty compact non horizontal Element of bool the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
f is non empty compact non vertical Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ (LSeg ((SE-corner f),(NE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
A1 is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = E-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
LSeg ((NW-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = W-bound f & b₁ `2 <= N-bound f & S-bound f <= b₁ `2 ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is non empty compact non horizontal Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(SE-corner f))) /\ (LSeg ((NW-corner f),(NE-corner f))) is compact Element of bool the carrier of (TOP-REAL 2)
A1 is set
LSeg ((NE-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = N-bound f ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= E-bound f & W-bound f <= b₁ `1 & b₁ `2 = S-bound f ) } is set
A2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 `1 is V11() real ext-real Element of REAL
A2 `2 is V11() real ext-real Element of REAL
a1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a1 `1 is V11() real ext-real Element of REAL
a1 `2 is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
3 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f) /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom <*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f) /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom <*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f) /. 3 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom <*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 3 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f) /. 4 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom <*(SW-corner f),(NW-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
len <*(NW-corner f),(NE-corner f),(SE-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(f) /. ((len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f) /. 5 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom <*(SW-corner f),(NW-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
len <*(NW-corner f),(NE-corner f),(SE-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(f) /. ((len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) + 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len <*(NW-corner f),(NE-corner f),(SE-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len <*(SW-corner f),(NW-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) + (len <*(SW-corner f),(NW-corner f)*>) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(len <*(SW-corner f),(NW-corner f)*>) + 3 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
2 + 3 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
f is Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*(NW-corner f),(NE-corner f),(SE-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. (len <*(NW-corner f),(NE-corner f),(SE-corner f)*>) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
L~ <*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*(NW-corner f),(NE-corner f),(SE-corner f)*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(NW-corner f),(NE-corner f),(SE-corner f)*> ) } is set
union { (LSeg (<*(NW-corner f),(NE-corner f),(SE-corner f)*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(NW-corner f),(NE-corner f),(SE-corner f)*> ) } is set
(L~ <*(NW-corner f),(NE-corner f),(SE-corner f)*>) \/ (LSeg ((SE-corner f),(SW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ <*(SW-corner f),(NW-corner f)*> is non empty compact Element of bool the carrier of (TOP-REAL 2)
len <*(SW-corner f),(NW-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (<*(SW-corner f),(NW-corner f)*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(SW-corner f),(NW-corner f)*> ) } is set
union { (LSeg (<*(SW-corner f),(NW-corner f)*>,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(SW-corner f),(NW-corner f)*> ) } is set
((L~ <*(NW-corner f),(NE-corner f),(SE-corner f)*>) \/ (LSeg ((SE-corner f),(SW-corner f)))) \/ (L~ <*(SW-corner f),(NW-corner f)*>) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ <*(NW-corner f),(NE-corner f),(SE-corner f)*>) \/ (LSeg ((SE-corner f),(SW-corner f)))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ (LSeg ((SE-corner f),(SW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ (LSeg ((SE-corner f),(SW-corner f)))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty compact non vertical Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty compact non horizontal Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(f) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(S-bound f),(N-bound f)*> is non empty non trivial V19() V22( NAT ) V23( REAL ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
A1 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
K105(<*(S-bound f),(N-bound f)*>) is non empty non trivial set
A2 is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
K513(<*(S-bound f),(N-bound f)*>,A2) is V11() real ext-real Element of REAL
K513(<*(S-bound f),(N-bound f)*>,A1) is V11() real ext-real Element of REAL
dom <*(S-bound f),(N-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
len <*(S-bound f),(N-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
<*(S-bound f),(N-bound f)*> . A2 is V11() real ext-real set
<*(S-bound f),(N-bound f)*> . A1 is V11() real ext-real set
(|[(W-bound f),(S-bound f)]|,|[(W-bound f),(N-bound f)]|) ][ (|[(E-bound f),(S-bound f)]|,|[(E-bound f),(N-bound f)]|) is V19() V22( NAT ) V23(K257( the carrier of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular Matrix of 2,2, the carrier of (TOP-REAL 2)
<*(N-bound f),(N-bound f),(S-bound f)*> is non empty non trivial V19() V22( NAT ) V23( REAL ) Function-like V32() 3 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
<*(W-bound f),(E-bound f),(E-bound f)*> is non empty non trivial V19() V22( NAT ) V23( REAL ) Function-like V32() 3 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
<*(W-bound f),(W-bound f)*> is non empty non trivial V19() V22( NAT ) V23( REAL ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
<*(W-bound f),(E-bound f),(E-bound f)*> ^ <*(W-bound f),(W-bound f)*> is non empty V19() V22( NAT ) V23( REAL ) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
rng <*(W-bound f),(W-bound f)*> is V199() V200() V201() Element of bool REAL
{(W-bound f),(W-bound f)} is non empty V199() V200() V201() set
{(W-bound f)} is non empty trivial V199() V200() V201() Element of bool REAL
rng <*(W-bound f),(E-bound f),(E-bound f)*> is V199() V200() V201() Element of bool REAL
{(W-bound f),(E-bound f),(E-bound f)} is non empty V199() V200() V201() set
{(E-bound f),(E-bound f),(W-bound f)} is non empty V199() V200() V201() set
{(W-bound f),(E-bound f)} is non empty V199() V200() V201() set
Xf is V19() V22( NAT ) V23( REAL ) Function-like V32() FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
rng Xf is V199() V200() V201() Element of bool REAL
{(W-bound f),(E-bound f)} \/ {(W-bound f)} is non empty V199() V200() V201() set
{(W-bound f),(W-bound f),(E-bound f)} is non empty V199() V200() V201() set
<*(W-bound f),(E-bound f)*> is non empty non trivial V19() V22( NAT ) V23( REAL ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
rng <*(W-bound f),(E-bound f)*> is V199() V200() V201() Element of bool REAL
Yf is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
K105(<*(W-bound f),(E-bound f)*>) is non empty non trivial set
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
K513(<*(W-bound f),(E-bound f)*>,n) is V11() real ext-real Element of REAL
K513(<*(W-bound f),(E-bound f)*>,Yf) is V11() real ext-real Element of REAL
dom <*(W-bound f),(E-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
len <*(W-bound f),(E-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
<*(W-bound f),(E-bound f)*> . n is V11() real ext-real set
<*(W-bound f),(E-bound f)*> . Yf is V11() real ext-real set
<*(N-bound f),(N-bound f),(S-bound f)*> ^ <*(S-bound f),(N-bound f)*> is non empty V19() V22( NAT ) V23( REAL ) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
rng <*(S-bound f),(N-bound f)*> is V199() V200() V201() Element of bool REAL
{(S-bound f),(N-bound f)} is non empty V199() V200() V201() set
rng <*(N-bound f),(N-bound f),(S-bound f)*> is V199() V200() V201() Element of bool REAL
{(N-bound f),(N-bound f),(S-bound f)} is non empty V199() V200() V201() set
Yf is V19() V22( NAT ) V23( REAL ) Function-like V32() FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
rng Yf is V199() V200() V201() Element of bool REAL
{(S-bound f),(N-bound f)} \/ {(S-bound f),(N-bound f)} is non empty V199() V200() V201() set
len <*(S-bound f),(N-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
card (rng Yf) is cardinal set
len <*(N-bound f),(N-bound f),(S-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom <*(N-bound f),(N-bound f),(S-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
Yf . 1 is V11() real ext-real set
<*(N-bound f),(N-bound f),(S-bound f)*> . 1 is V11() real ext-real set
len Yf is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
3 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
dom <*(S-bound f),(N-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
Yf . (3 + 2) is V11() real ext-real set
<*(S-bound f),(N-bound f)*> . 2 is V11() real ext-real set
Yf . 3 is V11() real ext-real set
<*(N-bound f),(N-bound f),(S-bound f)*> . 3 is V11() real ext-real set
Yf . 2 is V11() real ext-real set
<*(N-bound f),(N-bound f),(S-bound f)*> . 2 is V11() real ext-real set
len <*(NW-corner f),(NE-corner f),(SE-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom <*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
(f) /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(f) /. 3 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 3 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(f) /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
len <*(SW-corner f),(NW-corner f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len (<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*>) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom <*(SW-corner f),(NW-corner f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
3 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(f) /. (3 + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
LSeg ((f),3) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(f) /. (3 + 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
n is ordinal natural V11() real ext-real non negative set
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
(f) /. (n + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. (n + 1)) `1 is V11() real ext-real Element of REAL
((f) /. n) `2 is V11() real ext-real Element of REAL
((f) /. (n + 1)) `2 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
4 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
((f) /. 1) `2 is V11() real ext-real Element of REAL
(f) /. (1 + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. (1 + 1)) `2 is V11() real ext-real Element of REAL
((f) /. 2) `1 is V11() real ext-real Element of REAL
(f) /. (2 + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. (2 + 1)) `1 is V11() real ext-real Element of REAL
((f) /. 3) `2 is V11() real ext-real Element of REAL
((f) /. (3 + 1)) `2 is V11() real ext-real Element of REAL
(f) /. 4 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. 4) `1 is V11() real ext-real Element of REAL
(f) /. (4 + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. (4 + 1)) `1 is V11() real ext-real Element of REAL
4 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
LSeg ((f),4) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
LSeg ((f),2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
Yf . (3 + 1) is V11() real ext-real set
<*(S-bound f),(N-bound f)*> . 1 is V11() real ext-real set
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom Yf is V199() V200() V201() V202() V203() V204() bounded_below Element of bool NAT
Yf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `2 is V11() real ext-real Element of REAL
Yf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `2 is V11() real ext-real Element of REAL
Yf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `2 is V11() real ext-real Element of REAL
Yf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `2 is V11() real ext-real Element of REAL
Yf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `2 is V11() real ext-real Element of REAL
Y_axis (f) is non empty V19() V22( NAT ) V23( REAL ) Function-like V32() FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
Incr (Y_axis (f)) is non empty V19() V22( NAT ) V23( REAL ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like V189() V190() V191() increasing V195() FinSequence of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
LSeg ((f),1) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
n is ordinal natural V11() real ext-real non negative set
n + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
LSeg ((f),n) is Element of bool the carrier of (TOP-REAL 2)
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
LSeg ((f),(n + 1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((f),n)) /\ (LSeg ((f),(n + 1))) is Element of bool the carrier of (TOP-REAL 2)
(f) /. (n + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
{((f) /. (n + 1))} is non empty trivial set
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
2 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
LSeg ((f),n) is Element of bool the carrier of (TOP-REAL 2)
m is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
m + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
LSeg ((f),m) is Element of bool the carrier of (TOP-REAL 2)
0 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
n + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
2 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(n + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
n + (1 + 1) is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
0 + 2 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(LSeg ((f),n)) /\ (LSeg ((f),m)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((f),n)) /\ (LSeg ((f),m)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((f),n)) /\ (LSeg ((f),m)) is Element of bool the carrier of (TOP-REAL 2)
len <*(W-bound f),(E-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
card (rng Xf) is cardinal set
len <*(W-bound f),(E-bound f),(E-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom <*(W-bound f),(E-bound f),(E-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
Xf . 1 is V11() real ext-real set
<*(W-bound f),(E-bound f),(E-bound f)*> . 1 is V11() real ext-real set
len <*(W-bound f),(W-bound f)*> is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len Xf is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom <*(W-bound f),(W-bound f)*> is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
Xf . (3 + 2) is V11() real ext-real set
<*(W-bound f),(W-bound f)*> . 2 is V11() real ext-real set
Xf . 3 is V11() real ext-real set
<*(W-bound f),(E-bound f),(E-bound f)*> . 3 is V11() real ext-real set
Xf . 2 is V11() real ext-real set
<*(W-bound f),(E-bound f),(E-bound f)*> . 2 is V11() real ext-real set
Xf . (3 + 1) is V11() real ext-real set
<*(W-bound f),(W-bound f)*> . 1 is V11() real ext-real set
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
dom Xf is V199() V200() V201() V202() V203() V204() bounded_below Element of bool NAT
Xf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
Xf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
Xf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
Xf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
Xf . n is V11() real ext-real set
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((f) /. n) `1 is V11() real ext-real Element of REAL
X_axis (f) is non empty V19() V22( NAT ) V23( REAL ) Function-like V32() FinSequence-like FinSubsequence-like V189() V190() V191() FinSequence of REAL
Incr (X_axis (f)) is non empty V19() V22( NAT ) V23( REAL ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like V189() V190() V191() increasing V195() FinSequence of REAL
Indices ((|[(W-bound f),(S-bound f)]|,|[(W-bound f),(N-bound f)]|) ][ (|[(E-bound f),(S-bound f)]|,|[(E-bound f),(N-bound f)]|)) is set
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
m is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
[n,m] is non empty set
{n,m} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{n} is non empty trivial V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{n,m},{n}} is non empty set
((|[(W-bound f),(S-bound f)]|,|[(W-bound f),(N-bound f)]|) ][ (|[(E-bound f),(S-bound f)]|,|[(E-bound f),(N-bound f)]|)) * (n,m) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(Incr (X_axis (f))) . n is V11() real ext-real set
(Incr (Y_axis (f))) . m is V11() real ext-real set
|[((Incr (X_axis (f))) . n),((Incr (Y_axis (f))) . m)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
[:{1,2},{1,2}:] is non empty V23( RAT ) V23( INT ) V189() V190() V191() V192() set
{[1,1],[1,2],[2,1],[2,2]} is non empty set
width ((|[(W-bound f),(S-bound f)]|,|[(W-bound f),(N-bound f)]|) ][ (|[(E-bound f),(S-bound f)]|,|[(E-bound f),(N-bound f)]|)) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len (Incr (Y_axis (f))) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len ((|[(W-bound f),(S-bound f)]|,|[(W-bound f),(N-bound f)]|) ][ (|[(E-bound f),(S-bound f)]|,|[(E-bound f),(N-bound f)]|)) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
len (Incr (X_axis (f))) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
GoB ((Incr (X_axis (f))),(Incr (Y_axis (f)))) is V19() non empty-yielding V22( NAT ) V23(K257( the carrier of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K257( the carrier of (TOP-REAL 2))
GoB (f) is V19() non empty-yielding V22( NAT ) V23(K257( the carrier of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K257( the carrier of (TOP-REAL 2))
(GoB (f)) * (2,2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(f) /. 4 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(GoB (f)) * (1,1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(GoB (f)) * (2,1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(GoB (f)) * (1,2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
dom (f) is non empty non trivial V199() V200() V201() V202() V203() V204() left_end bounded_below Element of bool NAT
Indices (GoB (f)) is set
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
n is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
(f) /. n is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(f) /. (n + 1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
m is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
k is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
[m,k] is non empty set
{m,k} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{m} is non empty trivial V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{m,k},{m}} is non empty set
i is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
j is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
[i,j] is non empty set
{i,j} is non empty V199() V200() V201() V202() V203() V204() left_end bounded_below set
{i} is non empty trivial V199() V200() V201() V202() V203() V204() left_end bounded_below set
{{i,j},{i}} is non empty set
(GoB (f)) * (m,k) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(GoB (f)) * (i,j) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
m - i is V11() real ext-real set
abs (m - i) is V11() real ext-real Element of REAL
k - j is V11() real ext-real set
abs (k - j) is V11() real ext-real Element of REAL
(abs (m - i)) + (abs (k - j)) is V11() real ext-real set
(abs (m - i)) + (abs (k - j)) is V11() real ext-real Element of REAL
(abs (m - i)) + (abs (k - j)) is V11() real ext-real Element of REAL
(abs (m - i)) + (abs (k - j)) is V11() real ext-real Element of REAL
(abs (m - i)) + (abs (k - j)) is V11() real ext-real Element of REAL
f is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(f) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
[.(W-bound f),(E-bound f),(S-bound f),(N-bound f).] is non empty compact Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg ((SW-corner f),(NW-corner f))) \/ ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((SW-corner f),(NW-corner f))) \/ ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) \/ (LSeg ((SE-corner f),(SW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg ((SW-corner f),(NW-corner f))) \/ (LSeg ((NW-corner f),(NE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((SW-corner f),(NW-corner f))) \/ (LSeg ((NW-corner f),(NE-corner f)))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(((LSeg ((SW-corner f),(NW-corner f))) \/ (LSeg ((NW-corner f),(NE-corner f)))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ (LSeg ((SE-corner f),(SW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg ((NE-corner f),(SE-corner f))) \/ (LSeg ((SE-corner f),(SW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((SW-corner f),(NW-corner f))) \/ (LSeg ((NW-corner f),(NE-corner f)))) \/ ((LSeg ((NE-corner f),(SE-corner f))) \/ (LSeg ((SE-corner f),(SW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
bool the carrier of f is non empty set
[: the carrier of f,REAL:] is non empty V189() V190() V191() set
bool [: the carrier of f,REAL:] is non empty set
A2 is V19() V22( the carrier of f) V23( REAL ) Function-like V44( the carrier of f, REAL ) V189() V190() V191() continuous Element of bool [: the carrier of f,REAL:]
A1 is non empty compact Element of bool the carrier of f
A2 .: A1 is non empty V199() V200() V201() Element of bool REAL
f | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of f
the carrier of (f | A1) is non empty set
A2 | A1 is V19() V22( the carrier of (f | A1)) V23( REAL ) Function-like V44( the carrier of (f | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of (f | A1)) V267( the carrier of (f | A1)) V268() Element of bool [: the carrier of (f | A1),REAL:]
[: the carrier of (f | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of (f | A1),REAL:] is non empty set
(A2 | A1) .: the carrier of (f | A1) is V199() V200() V201() Element of bool REAL
(A2 | A1) .: A1 is V199() V200() V201() Element of bool REAL
f | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of f
the carrier of (f | A1) is non empty set
A2 | A1 is V19() V22( the carrier of (f | A1)) V23( REAL ) Function-like V44( the carrier of (f | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of (f | A1)) V267( the carrier of (f | A1)) V268() Element of bool [: the carrier of (f | A1),REAL:]
[: the carrier of (f | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of (f | A1),REAL:] is non empty set
(A2 | A1) .: the carrier of (f | A1) is V199() V200() V201() Element of bool REAL
(A2 | A1) .: A1 is V199() V200() V201() Element of bool REAL
f is Element of bool the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
proj1 .: f is V199() V200() V201() Element of bool REAL
lower_bound (proj1 .: f) is V11() real ext-real Element of REAL
rng (proj1 | f) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj1 | f)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
proj2 .: f is V199() V200() V201() Element of bool REAL
lower_bound (proj2 .: f) is V11() real ext-real Element of REAL
rng (proj2 | f) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj2 | f)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
proj2 .: f is V199() V200() V201() Element of bool REAL
upper_bound (proj2 .: f) is V11() real ext-real Element of REAL
rng (proj2 | f) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj2 | f)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
proj1 .: f is V199() V200() V201() Element of bool REAL
upper_bound (proj1 .: f) is V11() real ext-real Element of REAL
rng (proj1 | f) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj1 | f)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
A1 is non empty compact Element of bool the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
A2 is non empty compact Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is non empty Element of bool the carrier of (TOP-REAL 2)
W-bound A2 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A2 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A2 is V19() V22( the carrier of ((TOP-REAL 2) | A2)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A2), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A2)) V267( the carrier of ((TOP-REAL 2) | A2)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A2),REAL:]
the carrier of ((TOP-REAL 2) | A2) is non empty set
[: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty set
lower_bound (proj1 | A2) is V11() real ext-real Element of REAL
(proj1 | A2) .: the carrier of ((TOP-REAL 2) | A2) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A2) .: the carrier of ((TOP-REAL 2) | A2)) is V11() real ext-real Element of REAL
min ((W-bound A1),(W-bound A2)) is V11() real ext-real set
proj1 .: A1 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
lower_bound (proj1 .: A1) is V11() real ext-real Element of REAL
inf (proj1 .: A1) is V11() real ext-real set
proj1 .: A2 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
lower_bound (proj1 .: A2) is V11() real ext-real Element of REAL
inf (proj1 .: A2) is V11() real ext-real set
proj1 .: f is V199() V200() V201() Element of bool REAL
lower_bound (proj1 .: f) is V11() real ext-real Element of REAL
(proj1 .: A1) \/ (proj1 .: A2) is non empty V199() V200() V201() Element of bool REAL
lower_bound ((proj1 .: A1) \/ (proj1 .: A2)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
A1 is non empty compact Element of bool the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
A2 is non empty compact Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is non empty Element of bool the carrier of (TOP-REAL 2)
S-bound A2 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A2 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | A2 is V19() V22( the carrier of ((TOP-REAL 2) | A2)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A2), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A2)) V267( the carrier of ((TOP-REAL 2) | A2)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A2),REAL:]
the carrier of ((TOP-REAL 2) | A2) is non empty set
[: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty set
lower_bound (proj2 | A2) is V11() real ext-real Element of REAL
(proj2 | A2) .: the carrier of ((TOP-REAL 2) | A2) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | A2) .: the carrier of ((TOP-REAL 2) | A2)) is V11() real ext-real Element of REAL
min ((S-bound A1),(S-bound A2)) is V11() real ext-real set
proj2 .: A1 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
lower_bound (proj2 .: A1) is V11() real ext-real Element of REAL
inf (proj2 .: A1) is V11() real ext-real set
proj2 .: A2 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
lower_bound (proj2 .: A2) is V11() real ext-real Element of REAL
inf (proj2 .: A2) is V11() real ext-real set
proj2 .: f is V199() V200() V201() Element of bool REAL
lower_bound (proj2 .: f) is V11() real ext-real Element of REAL
(proj2 .: A1) \/ (proj2 .: A2) is non empty V199() V200() V201() Element of bool REAL
lower_bound ((proj2 .: A1) \/ (proj2 .: A2)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
A1 is non empty compact Element of bool the carrier of (TOP-REAL 2)
N-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
A2 is non empty compact Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is non empty Element of bool the carrier of (TOP-REAL 2)
N-bound A2 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A2 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | A2 is V19() V22( the carrier of ((TOP-REAL 2) | A2)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A2), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A2)) V267( the carrier of ((TOP-REAL 2) | A2)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A2),REAL:]
the carrier of ((TOP-REAL 2) | A2) is non empty set
[: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty set
upper_bound (proj2 | A2) is V11() real ext-real Element of REAL
(proj2 | A2) .: the carrier of ((TOP-REAL 2) | A2) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A2) .: the carrier of ((TOP-REAL 2) | A2)) is V11() real ext-real Element of REAL
max ((N-bound A1),(N-bound A2)) is V11() real ext-real set
proj2 .: A1 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
upper_bound (proj2 .: A1) is V11() real ext-real Element of REAL
sup (proj2 .: A1) is V11() real ext-real set
proj2 .: A2 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
upper_bound (proj2 .: A2) is V11() real ext-real Element of REAL
sup (proj2 .: A2) is V11() real ext-real set
proj2 .: f is V199() V200() V201() Element of bool REAL
upper_bound (proj2 .: f) is V11() real ext-real Element of REAL
(proj2 .: A1) \/ (proj2 .: A2) is non empty V199() V200() V201() Element of bool REAL
upper_bound ((proj2 .: A1) \/ (proj2 .: A2)) is V11() real ext-real Element of REAL
f is Element of bool the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
A1 is non empty compact Element of bool the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
A2 is non empty compact Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is non empty Element of bool the carrier of (TOP-REAL 2)
E-bound A2 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A2 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A2 is V19() V22( the carrier of ((TOP-REAL 2) | A2)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A2), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A2)) V267( the carrier of ((TOP-REAL 2) | A2)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A2),REAL:]
the carrier of ((TOP-REAL 2) | A2) is non empty set
[: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A2),REAL:] is non empty set
upper_bound (proj1 | A2) is V11() real ext-real Element of REAL
(proj1 | A2) .: the carrier of ((TOP-REAL 2) | A2) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | A2) .: the carrier of ((TOP-REAL 2) | A2)) is V11() real ext-real Element of REAL
max ((E-bound A1),(E-bound A2)) is V11() real ext-real set
proj1 .: A1 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
upper_bound (proj1 .: A1) is V11() real ext-real Element of REAL
sup (proj1 .: A1) is V11() real ext-real set
proj1 .: A2 is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
upper_bound (proj1 .: A2) is V11() real ext-real Element of REAL
sup (proj1 .: A2) is V11() real ext-real set
proj1 .: f is V199() V200() V201() Element of bool REAL
upper_bound (proj1 .: f) is V11() real ext-real Element of REAL
(proj1 .: A1) \/ (proj1 .: A2) is non empty V199() V200() V201() Element of bool REAL
upper_bound ((proj1 .: A1) \/ (proj1 .: A2)) is V11() real ext-real Element of REAL
f is V11() real ext-real set
A1 is V11() real ext-real set
[.f,A1.] is V199() V200() V201() V245() Element of bool REAL
A2 is ext-real set
A2 is ext-real set
A2 is V199() V200() V201() Element of bool REAL
f is V11() real ext-real Element of REAL
A1 is V11() real ext-real Element of REAL
[.f,A1.] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
A2 is V11() real ext-real Element of REAL
{f} is non empty trivial V199() V200() V201() Element of bool REAL
a1 is V11() real ext-real Element of REAL
a2 is V11() real ext-real Element of REAL
a2 * f is V11() real ext-real Element of REAL
1 - a2 is V11() real ext-real Element of REAL
(1 - a2) * A1 is V11() real ext-real Element of REAL
(a2 * f) + ((1 - a2) * A1) is V11() real ext-real Element of REAL
a1 is V11() real ext-real Element of REAL
a1 * f is V11() real ext-real Element of REAL
1 - a1 is V11() real ext-real Element of REAL
(1 - a1) * A1 is V11() real ext-real Element of REAL
(a1 * f) + ((1 - a1) * A1) is V11() real ext-real Element of REAL
A1 - A2 is V11() real ext-real Element of REAL
A1 - f is V11() real ext-real Element of REAL
(A1 - A2) / (A1 - f) is V11() real ext-real Element of REAL
a1 is V11() real ext-real Element of REAL
A2 * (A1 - f) is V11() real ext-real Element of REAL
(A2 * (A1 - f)) / (A1 - f) is V11() real ext-real Element of REAL
(A1 - A2) * f is V11() real ext-real Element of REAL
A2 - f is V11() real ext-real Element of REAL
(A2 - f) * A1 is V11() real ext-real Element of REAL
((A1 - A2) * f) + ((A2 - f) * A1) is V11() real ext-real Element of REAL
(((A1 - A2) * f) + ((A2 - f) * A1)) / (A1 - f) is V11() real ext-real Element of REAL
((A1 - A2) * f) / (A1 - f) is V11() real ext-real Element of REAL
((A2 - f) * A1) / (A1 - f) is V11() real ext-real Element of REAL
(((A1 - A2) * f) / (A1 - f)) + (((A2 - f) * A1) / (A1 - f)) is V11() real ext-real Element of REAL
(A2 - f) / (A1 - f) is V11() real ext-real Element of REAL
((A2 - f) / (A1 - f)) * A1 is V11() real ext-real Element of REAL
(((A1 - A2) * f) / (A1 - f)) + (((A2 - f) / (A1 - f)) * A1) is V11() real ext-real Element of REAL
((A1 - A2) / (A1 - f)) * f is V11() real ext-real Element of REAL
1 * (A1 - f) is V11() real ext-real Element of REAL
(1 * (A1 - f)) - (A1 - A2) is V11() real ext-real Element of REAL
((1 * (A1 - f)) - (A1 - A2)) / (A1 - f) is V11() real ext-real Element of REAL
(((1 * (A1 - f)) - (A1 - A2)) / (A1 - f)) * A1 is V11() real ext-real Element of REAL
(((A1 - A2) / (A1 - f)) * f) + ((((1 * (A1 - f)) - (A1 - A2)) / (A1 - f)) * A1) is V11() real ext-real Element of REAL
a1 * f is V11() real ext-real Element of REAL
1 - a1 is V11() real ext-real Element of REAL
(1 - a1) * A1 is V11() real ext-real Element of REAL
(a1 * f) + ((1 - a1) * A1) is V11() real ext-real Element of REAL
a1 is V11() real ext-real Element of REAL
a1 * f is V11() real ext-real Element of REAL
1 - a1 is V11() real ext-real Element of REAL
(1 - a1) * A1 is V11() real ext-real Element of REAL
(a1 * f) + ((1 - a1) * A1) is V11() real ext-real Element of REAL
a1 * A1 is V11() real ext-real Element of REAL
(a1 * A1) + ((1 - a1) * A1) is V11() real ext-real Element of REAL
1 * A1 is V11() real ext-real Element of REAL
(1 - a1) * f is V11() real ext-real Element of REAL
(a1 * f) + ((1 - a1) * f) is V11() real ext-real Element of REAL
1 * f is V11() real ext-real Element of REAL
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `1 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj1 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `1),(A1 `1).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
dom proj1 is Element of bool the carrier of (TOP-REAL 2)
A2 is set
a1 is V11() real ext-real Element of REAL
a2 is V11() real ext-real Element of REAL
a2 * (f `1) is V11() real ext-real Element of REAL
1 - a2 is V11() real ext-real Element of REAL
(1 - a2) * (A1 `1) is V11() real ext-real Element of REAL
(a2 * (f `1)) + ((1 - a2) * (A1 `1)) is V11() real ext-real Element of REAL
a2 * f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(1 - a2) * A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(a2 * f) + ((1 - a2) * A1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 is set
x is set
LSeg (A1,f) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * A1) + (b₁ * f)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(a2 * f) `1 is V11() real ext-real Element of REAL
((a2 * f) `1) + ((1 - a2) * (A1 `1)) is V11() real ext-real Element of REAL
((1 - a2) * A1) `1 is V11() real ext-real Element of REAL
((a2 * f) `1) + (((1 - a2) * A1) `1) is V11() real ext-real Element of REAL
((a2 * f) + ((1 - a2) * A1)) `1 is V11() real ext-real Element of REAL
proj1 . x is V11() real ext-real set
a1 is set
proj1 . a1 is V11() real ext-real set
a2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ is V11() real ext-real Element of REAL
1 - c₆ is V11() real ext-real Element of REAL
(1 - c₆) * A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ * f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((1 - c₆) * A1) + (c₆ * f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a2 `1 is V11() real ext-real Element of REAL
((1 - c₆) * A1) `1 is V11() real ext-real Element of REAL
(c₆ * f) `1 is V11() real ext-real Element of REAL
(((1 - c₆) * A1) `1) + ((c₆ * f) `1) is V11() real ext-real Element of REAL
(1 - c₆) * (A1 `1) is V11() real ext-real Element of REAL
((1 - c₆) * (A1 `1)) + ((c₆ * f) `1) is V11() real ext-real Element of REAL
c₆ * (f `1) is V11() real ext-real Element of REAL
((1 - c₆) * (A1 `1)) + (c₆ * (f `1)) is V11() real ext-real Element of REAL
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `2 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj2 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `2),(A1 `2).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
dom proj2 is Element of bool the carrier of (TOP-REAL 2)
A2 is set
a1 is V11() real ext-real Element of REAL
a2 is V11() real ext-real Element of REAL
a2 * (f `2) is V11() real ext-real Element of REAL
1 - a2 is V11() real ext-real Element of REAL
(1 - a2) * (A1 `2) is V11() real ext-real Element of REAL
(a2 * (f `2)) + ((1 - a2) * (A1 `2)) is V11() real ext-real Element of REAL
a2 * f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(1 - a2) * A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
(a2 * f) + ((1 - a2) * A1) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A2 is set
x is set
LSeg (A1,f) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * A1) + (b₁ * f)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(a2 * f) `2 is V11() real ext-real Element of REAL
((a2 * f) `2) + ((1 - a2) * (A1 `2)) is V11() real ext-real Element of REAL
((1 - a2) * A1) `2 is V11() real ext-real Element of REAL
((a2 * f) `2) + (((1 - a2) * A1) `2) is V11() real ext-real Element of REAL
((a2 * f) + ((1 - a2) * A1)) `2 is V11() real ext-real Element of REAL
proj2 . x is V11() real ext-real set
a1 is set
proj2 . a1 is V11() real ext-real set
a2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ is V11() real ext-real Element of REAL
1 - c₆ is V11() real ext-real Element of REAL
(1 - c₆) * A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
c₆ * f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
((1 - c₆) * A1) + (c₆ * f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
a2 `2 is V11() real ext-real Element of REAL
((1 - c₆) * A1) `2 is V11() real ext-real Element of REAL
(c₆ * f) `2 is V11() real ext-real Element of REAL
(((1 - c₆) * A1) `2) + ((c₆ * f) `2) is V11() real ext-real Element of REAL
(1 - c₆) * (A1 `2) is V11() real ext-real Element of REAL
((1 - c₆) * (A1 `2)) + ((c₆ * f) `2) is V11() real ext-real Element of REAL
c₆ * (f `2) is V11() real ext-real Element of REAL
((1 - c₆) * (A1 `2)) + (c₆ * (f `2)) is V11() real ext-real Element of REAL
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `1 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
W-bound (LSeg (f,A1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (f,A1)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg (f,A1)) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg (f,A1))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V267( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty set
lower_bound (proj1 | (LSeg (f,A1))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) is V11() real ext-real Element of REAL
proj1 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `1),(A1 `1).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound (proj1 .: (LSeg (f,A1))) is V11() real ext-real Element of REAL
inf (proj1 .: (LSeg (f,A1))) is V11() real ext-real set
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `2 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
S-bound (LSeg (f,A1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (f,A1)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg (f,A1)) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg (f,A1))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V267( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty set
lower_bound (proj2 | (LSeg (f,A1))) is V11() real ext-real Element of REAL
(proj2 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) is V11() real ext-real Element of REAL
proj2 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `2),(A1 `2).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound (proj2 .: (LSeg (f,A1))) is V11() real ext-real Element of REAL
inf (proj2 .: (LSeg (f,A1))) is V11() real ext-real set
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `2 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
N-bound (LSeg (f,A1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (f,A1)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg (f,A1)) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg (f,A1))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V267( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty set
upper_bound (proj2 | (LSeg (f,A1))) is V11() real ext-real Element of REAL
(proj2 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) is V11() real ext-real Element of REAL
proj2 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `2),(A1 `2).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound (proj2 .: (LSeg (f,A1))) is V11() real ext-real Element of REAL
sup (proj2 .: (LSeg (f,A1))) is V11() real ext-real set
f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
A1 `1 is V11() real ext-real Element of REAL
LSeg (f,A1) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * A1)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
E-bound (LSeg (f,A1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (f,A1)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg (f,A1)) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg (f,A1))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V267( the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))),REAL:] is non empty set
upper_bound (proj1 | (LSeg (f,A1))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (LSeg (f,A1))) .: the carrier of ((TOP-REAL 2) | (LSeg (f,A1)))) is V11() real ext-real Element of REAL
proj1 .: (LSeg (f,A1)) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(f `1),(A1 `1).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound (proj1 .: (LSeg (f,A1))) is V11() real ext-real Element of REAL
sup (proj1 .: (LSeg (f,A1))) is V11() real ext-real set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(SE-corner f) `1 is V11() real ext-real Element of REAL
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(NE-corner f) `1 is V11() real ext-real Element of REAL
W-bound (LSeg ((NE-corner f),(SE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((NE-corner f),(SE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty set
lower_bound (proj1 | (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(SW-corner f) `1 is V11() real ext-real Element of REAL
(NW-corner f) `1 is V11() real ext-real Element of REAL
W-bound (LSeg ((SW-corner f),(NW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((SW-corner f),(NW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty set
lower_bound (proj1 | (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
W-bound ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty set
lower_bound (proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) is V11() real ext-real Element of REAL
W-bound (LSeg ((SE-corner f),(SW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((SE-corner f),(SW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty set
lower_bound (proj1 | (LSeg ((SE-corner f),(SW-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg ((SE-corner f),(SW-corner f)))),(W-bound (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real set
min ((W-bound f),(W-bound f)) is V11() real ext-real set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
W-bound ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty set
lower_bound (proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) is V11() real ext-real Element of REAL
W-bound (LSeg ((NW-corner f),(NE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((NW-corner f),(NE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty set
lower_bound (proj1 | (LSeg ((NW-corner f),(NE-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg ((NW-corner f),(NE-corner f)))),(W-bound (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real set
min ((E-bound f),(W-bound f)) is V11() real ext-real set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
S-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(SE-corner f) `2 is V11() real ext-real Element of REAL
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(NE-corner f) `2 is V11() real ext-real Element of REAL
S-bound (LSeg ((NE-corner f),(SE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((NE-corner f),(SE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty set
lower_bound (proj2 | (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
S-bound (LSeg ((SW-corner f),(NW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((SW-corner f),(NW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty set
lower_bound (proj2 | (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
S-bound ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty set
lower_bound (proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) is V11() real ext-real Element of REAL
S-bound (LSeg ((SE-corner f),(SW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((SE-corner f),(SW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty set
lower_bound (proj2 | (LSeg ((SE-corner f),(SW-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) is V11() real ext-real Element of REAL
min ((S-bound (LSeg ((SE-corner f),(SW-corner f)))),(S-bound (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real set
min ((S-bound f),(S-bound f)) is V11() real ext-real set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
S-bound ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty set
lower_bound (proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) is V11() real ext-real Element of REAL
S-bound (LSeg ((NW-corner f),(NE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((NW-corner f),(NE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty set
lower_bound (proj2 | (LSeg ((NW-corner f),(NE-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) is V11() real ext-real Element of REAL
min ((S-bound (LSeg ((NW-corner f),(NE-corner f)))),(S-bound (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real set
min ((N-bound f),(S-bound f)) is V11() real ext-real set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
N-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(NW-corner f) `2 is V11() real ext-real Element of REAL
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(SW-corner f) `2 is V11() real ext-real Element of REAL
N-bound (LSeg ((SW-corner f),(NW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((SW-corner f),(NW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty set
upper_bound (proj2 | (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
N-bound (LSeg ((NE-corner f),(SE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((NE-corner f),(SE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty set
upper_bound (proj2 | (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
N-bound ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty set
upper_bound (proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) is V11() real ext-real Element of REAL
N-bound (LSeg ((NW-corner f),(NE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((NW-corner f),(NE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty set
upper_bound (proj2 | (LSeg ((NW-corner f),(NE-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) is V11() real ext-real Element of REAL
max ((N-bound (LSeg ((NW-corner f),(NE-corner f)))),(N-bound (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real set
max ((N-bound f),(N-bound f)) is V11() real ext-real set
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
N-bound ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty set
upper_bound (proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) is V11() real ext-real Element of REAL
N-bound (LSeg ((SE-corner f),(SW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (LSeg ((SE-corner f),(SW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty set
upper_bound (proj2 | (LSeg ((SE-corner f),(SW-corner f)))) is V11() real ext-real Element of REAL
(proj2 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) is V11() real ext-real Element of REAL
max ((N-bound (LSeg ((SE-corner f),(SW-corner f)))),(N-bound (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real set
max ((S-bound f),(N-bound f)) is V11() real ext-real set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(NW-corner f) `1 is V11() real ext-real Element of REAL
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
(SW-corner f) `1 is V11() real ext-real Element of REAL
E-bound (LSeg ((SW-corner f),(NW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((SW-corner f),(NW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))),REAL:] is non empty set
upper_bound (proj1 | (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (LSeg ((SW-corner f),(NW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(SE-corner f) `1 is V11() real ext-real Element of REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
E-bound (LSeg ((NE-corner f),(SE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((NE-corner f),(SE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))),REAL:] is non empty set
upper_bound (proj1 | (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (LSeg ((NE-corner f),(SE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
E-bound ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))),REAL:] is non empty set
upper_bound (proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))))) is V11() real ext-real Element of REAL
E-bound (LSeg ((NW-corner f),(NE-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((NW-corner f),(NE-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))),REAL:] is non empty set
upper_bound (proj1 | (LSeg ((NW-corner f),(NE-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (LSeg ((NW-corner f),(NE-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((NW-corner f),(NE-corner f))))) is V11() real ext-real Element of REAL
max ((E-bound (LSeg ((NW-corner f),(NE-corner f)))),(E-bound (LSeg ((NE-corner f),(SE-corner f))))) is V11() real ext-real set
max ((E-bound f),(E-bound f)) is V11() real ext-real set
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
E-bound ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is V19() V22( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is non empty set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))),REAL:] is non empty set
upper_bound (proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))))) .: the carrier of ((TOP-REAL 2) | ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))))) is V11() real ext-real Element of REAL
E-bound (LSeg ((SE-corner f),(SW-corner f))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (LSeg ((SE-corner f),(SW-corner f))) is V19() V22( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V267( the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))),REAL:] is non empty set
upper_bound (proj1 | (LSeg ((SE-corner f),(SW-corner f)))) is V11() real ext-real Element of REAL
(proj1 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (LSeg ((SE-corner f),(SW-corner f)))) .: the carrier of ((TOP-REAL 2) | (LSeg ((SE-corner f),(SW-corner f))))) is V11() real ext-real Element of REAL
max ((E-bound (LSeg ((SE-corner f),(SW-corner f)))),(E-bound (LSeg ((SW-corner f),(NW-corner f))))) is V11() real ext-real set
max ((W-bound f),(E-bound f)) is V11() real ext-real set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
N-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
N-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
|[(E-bound f),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
W-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (NW-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
N-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
N-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (f))),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ (f)))) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
S-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (SE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
E-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f))) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NW-corner f),(NE-corner f))) \/ (LSeg ((NE-corner f),(SE-corner f)))) \/ ((LSeg ((SE-corner f),(SW-corner f))) \/ (LSeg ((SW-corner f),(NW-corner f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (f))),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ (f)))) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj2 .: (LSeg ((SW-corner f),(NW-corner f))) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj1 .: (LSeg ((NW-corner f),(NE-corner f))) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
(NW-corner f) `1 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NE-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj2 .: (LSeg ((NE-corner f),(SE-corner f))) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(SW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (SW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
proj1 .: (LSeg ((SE-corner f),(SW-corner f))) is non empty V199() V200() V201() bounded_below bounded_above real-bounded Element of bool REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
(SW-corner f) `1 is V11() real ext-real Element of REAL
(SE-corner f) `1 is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
W-min (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
W-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (NW-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:] is non empty set
lower_bound (proj2 | (W-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (W-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(lower_bound (proj2 | (W-most (L~ (f)))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj2 | (W-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj2 | (W-most (L~ (f))))) is V11() real ext-real Element of REAL
proj2 .: (W-most (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound (proj2 .: (W-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound [.(S-bound f),(N-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
W-max (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
W-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (NW-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(NW-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))),REAL:] is non empty set
upper_bound (proj2 | (W-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (W-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(upper_bound (proj2 | (W-most (L~ (f)))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj2 | (W-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj2 | (W-most (L~ (f))))) is V11() real ext-real Element of REAL
proj2 .: (W-most (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound (proj2 .: (W-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound [.(S-bound f),(N-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
N-min (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
N-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (f))))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj1 | (N-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj1 | (N-most (L~ (f))))) is V11() real ext-real Element of REAL
proj1 .: (N-most (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound (proj1 .: (N-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound [.(W-bound f),(E-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
N-max (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
N-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))),REAL:] is non empty set
upper_bound (proj1 | (N-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (N-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (f))))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj1 | (N-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj1 | (N-most (L~ (f))))) is V11() real ext-real Element of REAL
proj1 .: (N-most (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound (proj1 .: (N-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound [.(W-bound f),(E-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
E-min (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
E-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:] is non empty set
lower_bound (proj2 | (E-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (E-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(lower_bound (proj2 | (E-most (L~ (f)))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj2 | (E-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj2 | (E-most (L~ (f))))) is V11() real ext-real Element of REAL
proj2 .: (E-most (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound (proj2 .: (E-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound [.(S-bound f),(N-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
E-max (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
E-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(N-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ (f)))) + (b₁ * (NE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ (f))),(NE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))),REAL:] is non empty set
upper_bound (proj2 | (E-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (E-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(upper_bound (proj2 | (E-most (L~ (f)))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj2 | (E-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj2 | (E-most (L~ (f))))) is V11() real ext-real Element of REAL
proj2 .: (E-most (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound (proj2 .: (E-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(S-bound f),(N-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound [.(S-bound f),(N-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
S-min (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (SE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:] is non empty set
lower_bound (proj1 | (S-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (S-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ (f))))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj1 | (S-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
lower_bound (rng (proj1 | (S-most (L~ (f))))) is V11() real ext-real Element of REAL
proj1 .: (S-most (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound (proj1 .: (S-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
lower_bound [.(W-bound f),(E-bound f).] is V11() real ext-real Element of REAL
f is non empty compact Element of bool the carrier of (TOP-REAL 2)
(f) is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (f) is compact Element of bool the carrier of (TOP-REAL 2)
len (f) is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
union { (LSeg ((f),b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f) ) } is set
S-max (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most (L~ (f)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (f))) is set
[: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:] is non empty set
lower_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
S-bound (L~ (f)) is V11() real ext-real Element of REAL
proj2 | (L~ (f)) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ (f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ (f))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (f))),REAL:]
lower_bound (proj2 | (L~ (f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ (f)) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (f))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (f))) .: the carrier of ((TOP-REAL 2) | (L~ (f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (f))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f)))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ (f)))) + (b₁ * (SE-corner (L~ (f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ (f))),(SE-corner (L~ (f))))) /\ (L~ (f)) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (f))) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most (L~ (f))))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))), REAL ) V189() V190() V191() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:] is V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))),REAL:] is non empty set
upper_bound (proj1 | (S-most (L~ (f)))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (S-most (L~ (f)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ (f))))),(S-bound (L~ (f)))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng (proj1 | (S-most (L~ (f)))) is V199() V200() V201() Element of bool REAL
upper_bound (rng (proj1 | (S-most (L~ (f))))) is V11() real ext-real Element of REAL
proj1 .: (S-most (L~ (f))) is V199() V200() V201() Element of bool REAL
upper_bound (proj1 .: (S-most (L~ (f)))) is V11() real ext-real Element of REAL
[.(W-bound f),(E-bound f).] is V199() V200() V201() bounded_below bounded_above real-bounded V245() Element of bool REAL
upper_bound [.(W-bound f),(E-bound f).] is V11() real ext-real Element of REAL
f is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(f) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
NW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is non empty set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
N-bound f is V11() real ext-real Element of REAL
proj2 | f is V19() V22( the carrier of ((TOP-REAL 2) | f)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | f), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | f)) V267( the carrier of ((TOP-REAL 2) | f)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
upper_bound ((proj1 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
lower_bound ((proj2 | f) .: the carrier of ((TOP-REAL 2) | f)) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner f is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound f),(S-bound f)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner f),(NW-corner f)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner f),(NE-corner f),(SE-corner f)*> ^ <*(SW-corner f),(NW-corner f)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
( the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V19() V22( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V267( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),REAL:]
the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is non empty set
[: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),REAL:] is non empty set
lower_bound (proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V11() real ext-real Element of REAL
(proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) is V11() real ext-real Element of REAL
N-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V11() real ext-real Element of REAL
proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V19() V22( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V267( the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),REAL:]
upper_bound (proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V11() real ext-real Element of REAL
(proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) is V11() real ext-real Element of REAL
|[(W-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(N-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V11() real ext-real Element of REAL
upper_bound (proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) is V11() real ext-real Element of REAL
|[(E-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(N-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is V11() real ext-real Element of REAL
lower_bound (proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) is V11() real ext-real Element of REAL
lower_bound ((proj2 | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)) .: the carrier of ((TOP-REAL 2) | the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))) is V11() real ext-real Element of REAL
|[(E-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(S-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(NE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(SE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(S-bound the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(NW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(NE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(SE-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))*> ^ <*(SW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)),(NW-corner the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2))*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like () FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
W-max (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is non empty set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 2 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-max (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is non empty set
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
E-max (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is non empty set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 3 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
S-max (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is non empty set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V199() V200() V201() Element of bool REAL
upper_bound ((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
E-min (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
NE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is non empty set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 4 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
S-min (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is non empty set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V19() V22( the carrier of ((TOP-REAL 2) | (L~ f))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (L~ f))) V267( the carrier of ((TOP-REAL 2) | (L~ f))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is non empty set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
W-min (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V258( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is compact Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V19() V22( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V267( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V268() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is non empty set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V199() V200() V201() Element of bool REAL
lower_bound ((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is V11() real ext-real Element of REAL
A1 is V11() real ext-real Element of REAL
A2 is V11() real ext-real Element of REAL
a1 is V11() real ext-real Element of REAL
[.f,A1,A2,a1.] is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = f & b₁ `2 <= a1 & A2 <= b₁ `2 ) or ( b₁ `1 <= A1 & f <= b₁ `1 & b₁ `2 = a1 ) or ( b₁ `1 <= A1 & f <= b₁ `1 & b₁ `2 = A2 ) or ( b₁ `1 = A1 & b₁ `2 <= a1 & A2 <= b₁ `2 ) ) } is set
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
A1 is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
(A1) is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
NW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
W-bound A1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | A1 is non empty strict TopSpace-like compact pseudocompact SubSpace of TOP-REAL 2
proj1 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
the carrier of ((TOP-REAL 2) | A1) is non empty set
[: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty V189() V190() V191() set
bool [: the carrier of ((TOP-REAL 2) | A1),REAL:] is non empty set
lower_bound (proj1 | A1) is V11() real ext-real Element of REAL
(proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
lower_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
N-bound A1 is V11() real ext-real Element of REAL
proj2 | A1 is V19() V22( the carrier of ((TOP-REAL 2) | A1)) V23( REAL ) Function-like V44( the carrier of ((TOP-REAL 2) | A1), REAL ) V189() V190() V191() continuous V260() V261() V266( the carrier of ((TOP-REAL 2) | A1)) V267( the carrier of ((TOP-REAL 2) | A1)) V268() Element of bool [: the carrier of ((TOP-REAL 2) | A1),REAL:]
upper_bound (proj2 | A1) is V11() real ext-real Element of REAL
(proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1) is V199() V200() V201() Element of bool REAL
upper_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(W-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
NE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
E-bound A1 is V11() real ext-real Element of REAL
upper_bound (proj1 | A1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(N-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
SE-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
S-bound A1 is V11() real ext-real Element of REAL
lower_bound (proj2 | A1) is V11() real ext-real Element of REAL
lower_bound ((proj2 | A1) .: the carrier of ((TOP-REAL 2) | A1)) is V11() real ext-real Element of REAL
|[(E-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
SW-corner A1 is 2 -element FinSequence-like V191() Element of the carrier of (TOP-REAL 2)
|[(W-bound A1),(S-bound A1)]| is non empty non trivial V19() V22( NAT ) Function-like V32() 2 -element FinSequence-like FinSubsequence-like V189() V190() V191() Element of the carrier of (TOP-REAL 2)
<*(SW-corner A1),(NW-corner A1)*> is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner A1),(NE-corner A1),(SE-corner A1)*> ^ <*(SW-corner A1),(NW-corner A1)*> is non empty V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like V32() 3 + 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
[.(W-bound A1),(E-bound A1),(S-bound A1),(N-bound A1).] is non empty compact Element of bool the carrier of (TOP-REAL 2)
f is Element of bool the carrier of (TOP-REAL 2)
f ` is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (f `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (f `)) is set
bool the carrier of ((TOP-REAL 2) | (f `)) is non empty set
A1 is Element of bool the carrier of (TOP-REAL 2)
A2 is Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is Element of bool the carrier of (TOP-REAL 2)
Cl A1 is Element of bool the carrier of (TOP-REAL 2)
(Cl A1) \ A1 is Element of bool the carrier of (TOP-REAL 2)
Cl A2 is Element of bool the carrier of (TOP-REAL 2)
(Cl A2) \ A2 is Element of bool the carrier of (TOP-REAL 2)
A2 /\ (f `) is Element of bool the carrier of (TOP-REAL 2)
A1 /\ (f `) is Element of bool the carrier of (TOP-REAL 2)
a2 is Element of bool the carrier of ((TOP-REAL 2) | (f `))
a1 is Element of bool the carrier of ((TOP-REAL 2) | (f `))
c₆ is Element of bool the carrier of (TOP-REAL 2)
A2 is Element of bool the carrier of (TOP-REAL 2)
c₆ \/ A2 is Element of bool the carrier of (TOP-REAL 2)
Cl c₆ is Element of bool the carrier of (TOP-REAL 2)
(Cl c₆) \ c₆ is Element of bool the carrier of (TOP-REAL 2)
Cl A2 is Element of bool the carrier of (TOP-REAL 2)
(Cl A2) \ A2 is Element of bool the carrier of (TOP-REAL 2)
A1 is Element of bool the carrier of (TOP-REAL 2)
A2 is Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is Element of bool the carrier of (TOP-REAL 2)
Cl A1 is Element of bool the carrier of (TOP-REAL 2)
(Cl A1) \ A1 is Element of bool the carrier of (TOP-REAL 2)
Cl A2 is Element of bool the carrier of (TOP-REAL 2)
(Cl A2) \ A2 is Element of bool the carrier of (TOP-REAL 2)
a2 is Element of bool the carrier of (TOP-REAL 2)
a1 is Element of bool the carrier of (TOP-REAL 2)
Cl a1 is Element of bool the carrier of (TOP-REAL 2)
(Cl a1) \ a1 is Element of bool the carrier of (TOP-REAL 2)
a1 \/ a2 is Element of bool the carrier of (TOP-REAL 2)
Cl a2 is Element of bool the carrier of (TOP-REAL 2)
(Cl a2) \ a2 is Element of bool the carrier of (TOP-REAL 2)
a1 /\ a2 is Element of bool the carrier of (TOP-REAL 2)
c₆ is Element of bool the carrier of ((TOP-REAL 2) | (f `))
A2 is Element of bool the carrier of ((TOP-REAL 2) | (f `))
x is Element of bool the carrier of ((TOP-REAL 2) | (f `))
f2 is Element of bool the carrier of ((TOP-REAL 2) | (f `))
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
LeftComp f is Element of bool the carrier of (TOP-REAL 2)
RightComp f is Element of bool the carrier of (TOP-REAL 2)
L~ f is non empty compact Jordan Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
{ (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
(L~ f) ` is Element of bool the carrier of (TOP-REAL 2)
(LeftComp f) \/ (RightComp f) is Element of bool the carrier of (TOP-REAL 2)
A1 is Element of bool the carrier of (TOP-REAL 2)
A2 is Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is Element of bool the carrier of (TOP-REAL 2)
Cl A1 is Element of bool the carrier of (TOP-REAL 2)
(Cl A1) \ A1 is Element of bool the carrier of (TOP-REAL 2)
Cl A2 is Element of bool the carrier of (TOP-REAL 2)
(Cl A2) \ A2 is Element of bool the carrier of (TOP-REAL 2)
{(LeftComp f),(RightComp f)} is non empty set
{A1,A2} is non empty set
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
LeftComp f is Element of bool the carrier of (TOP-REAL 2)
left_cell (f,1) is Element of bool the carrier of (TOP-REAL 2)
Int (left_cell (f,1)) is Element of bool the carrier of (TOP-REAL 2)
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
RightComp f is Element of bool the carrier of (TOP-REAL 2)
right_cell (f,1) is Element of bool the carrier of (TOP-REAL 2)
Int (right_cell (f,1)) is Element of bool the carrier of (TOP-REAL 2)
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V97() V188() V199() V200() V201() V202() V203() V204() left_end bounded_below Element of NAT
len f is ordinal natural V11() real ext-real non negative V97() V188() V199() V200() V201() V202() V203() V204() bounded_below Element of NAT
f is non empty non trivial V19() V22( NAT ) V23( the carrier of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
LeftComp f is non empty Element of bool the carrier of (TOP-REAL 2)
RightComp f is non empty Element of bool the carrier of (TOP-REAL 2)