:: EUCLIDLP semantic presentation

REAL is non empty V45() V46() V47() V51() V52() set
NAT is V45() V46() V47() V48() V49() V50() V51() Element of bool REAL
bool REAL is non empty set
COMPLEX is non empty V45() V51() V52() set
RAT is non empty V45() V46() V47() V48() V51() V52() set
INT is non empty V45() V46() V47() V48() V49() V51() V52() set
omega is V45() V46() V47() V48() V49() V50() V51() set
bool omega is non empty set
bool NAT is non empty set
[:COMPLEX,COMPLEX:] is non empty complex-yielding set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is non empty complex-yielding V34() V35() set
bool [:COMPLEX,REAL:] is non empty set
1 is non empty natural V11() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
[:1,1:] is non empty V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:[:1,1:],1:] is non empty set
[:[:1,1:],REAL:] is non empty complex-yielding V34() V35() set
bool [:[:1,1:],REAL:] is non empty set
[:REAL,REAL:] is non empty complex-yielding V34() V35() set
[:[:REAL,REAL:],REAL:] is non empty complex-yielding V34() V35() set
bool [:[:REAL,REAL:],REAL:] is non empty set
2 is non empty natural V11() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
[:2,2:] is non empty V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
[:[:2,2:],REAL:] is non empty complex-yielding V34() V35() set
bool [:[:2,2:],REAL:] is non empty set
bool [:REAL,REAL:] is non empty set
TOP-REAL 2 is V79() V105() V130() V157() V158() V159() V160() V161() V162() V163() V169() L15()
the U1 of (TOP-REAL 2) is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty set
[:RAT,RAT:] is non empty V20( RAT ) complex-yielding V34() V35() set
bool [:RAT,RAT:] is non empty set
[:[:RAT,RAT:],RAT:] is non empty V20( RAT ) complex-yielding V34() V35() set
bool [:[:RAT,RAT:],RAT:] is non empty set
[:INT,INT:] is non empty V20( RAT ) V20( INT ) complex-yielding V34() V35() set
bool [:INT,INT:] is non empty set
[:[:INT,INT:],INT:] is non empty V20( RAT ) V20( INT ) complex-yielding V34() V35() set
bool [:[:INT,INT:],INT:] is non empty set
[:NAT,NAT:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
[:[:NAT,NAT:],NAT:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:[:NAT,NAT:],NAT:] is non empty set
0 is empty natural V11() real ext-real non positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() Element of NAT
sqrt 0 is V11() real ext-real Element of REAL
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n / x1 is V11() real ext-real Element of REAL
1 / x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
n * x2 is V11() real ext-real Element of REAL
(n * x2) / x1 is V11() real ext-real Element of REAL
x2 / x1 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n / x1) * (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * x2) / x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 / x1) * (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x2 / x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n / x1) * x2 is V11() real ext-real Element of REAL
((n / x1) * x2) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 / x1) * x2 is V11() real ext-real Element of REAL
((1 / x1) * x2) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x1,K174(x1)) is V16() Function-like set
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is V11() real ext-real Element of REAL
- n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
- (n * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K38(1) is V11() real ext-real non positive set
K38(1) * (n * x2) is V16() Function-like set
(- n) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
- x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K38(1) * x2 is V16() Function-like set
n * (- x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * n is V11() real ext-real Element of REAL
((- 1) * n) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * (- 1) is V11() real ext-real Element of REAL
(n * (- 1)) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) * y1 is V16() Function-like set
K145(x2,K174(y1)) is V16() Function-like set
x1 - (x2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x2 - y1)) is V16() Function-like complex-yielding set
K38(1) * (x2 - y1) is V16() Function-like set
K145(x1,K174((x2 - y1))) is V16() Function-like set
(x1 - x2) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 - x2) - (- y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((- y1)) is V16() Function-like complex-yielding set
K38(1) * (- y1) is V16() Function-like set
K145((x1 - x2),K174((- y1))) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x2,K174(y1)) is V16() Function-like set
x1 + (x2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x1 + x2),K174(y1)) is V16() Function-like set
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + (- y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 + (- y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (y1 + (- y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x2 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- y1) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((- y1) + y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 + y1) + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (y1 + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (y1 + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * x2 is V16() Function-like set
(- x1) + (- x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((x1 + x2) + y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((x1 + x2) + y1) is V16() Function-like set
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * y1 is V16() Function-like set
((- x1) + (- x2)) + (- y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(0* n) - ((x1 + x2) + y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((x1 + x2) + y1)) is V16() Function-like complex-yielding set
K145((0* n),K174(((x1 + x2) + y1))) is V16() Function-like set
(0* n) - (x1 + x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x1 + x2)) is V16() Function-like complex-yielding set
K38(1) * (x1 + x2) is V16() Function-like set
K145((0* n),K174((x1 + x2))) is V16() Function-like set
((0* n) - (x1 + x2)) - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K145(((0* n) - (x1 + x2)),K174(y1)) is V16() Function-like set
(0* n) - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K145((0* n),K174(x1)) is V16() Function-like set
((0* n) - x1) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K145(((0* n) - x1),K174(x2)) is V16() Function-like set
(((0* n) - x1) - x2) - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((0* n) - x1) - x2),K174(y1)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
|.(x1 - x2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - x2),(x1 - x2)) is V16() Function-like set
K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
|((x1 - x2),(x1 - x2))| is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x2 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
x2 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x2,K174(y1)) is V16() Function-like set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
0* x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x1 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of x1 -tuples_on REAL
Seg x1 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg x1),0) is V16() V19( Seg x1) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg x1,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg x1),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg x1),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg x1),{0}:] is non empty set
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n - x1 is V11() real ext-real Element of REAL
- x1 is V11() real ext-real Element of REAL
x2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x2 is non empty FinSequence-membered FinSequenceSet of REAL
x2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x2 } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(n - x1) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
n * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(- x1) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(n * y1) + ((- x1) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
x1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
- (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K38(1) is V11() real ext-real non positive set
K38(1) * (x1 * y1) is V16() Function-like set
(n * y1) + (- (x1 * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(n * y1) - (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K174((x1 * y1)) is V16() Function-like complex-yielding set
K145((n * y1),K174((x1 * y1))) is V16() Function-like set
n + (- x1) is V11() real ext-real Element of REAL
(n + (- x1)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
n is V11() real ext-real Element of REAL
- n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x2,K174(y1)) is V16() Function-like set
n * (x2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
- (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K38(1) * (n * y1) is V16() Function-like set
(n * x2) + (- (n * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(- n) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * x2) + ((- n) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * x2) - (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K174((n * y1)) is V16() Function-like complex-yielding set
K145((n * x2),K174((n * y1))) is V16() Function-like set
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * (- y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * x2) + (n * (- y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n - x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(n - x1) - x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n - x1) - x2) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * y2) - (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((x1 * y2)) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (x1 * y2) is V16() Function-like set
K145((n * y2),K174((x1 * y2))) is V16() Function-like set
x2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * y2) - (x1 * y2)) - (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((x2 * y2)) is V16() Function-like complex-yielding set
K38(1) * (x2 * y2) is V16() Function-like set
K145(((n * y2) - (x1 * y2)),K174((x2 * y2))) is V16() Function-like set
(n - x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n - x1) * y2) - (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K145(((n - x1) * y2),K174((x2 * y2))) is V16() Function-like set
n is V11() real ext-real Element of REAL
- n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
- x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
- x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(- n) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(- x1) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((- n) * P) + ((- x1) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * P) + (x1 * L1)) + (x2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 - (((n * P) + (x1 * L1)) + (x2 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((((n * P) + (x1 * L1)) + (x2 * L2))) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (((n * P) + (x1 * L1)) + (x2 * L2)) is V16() Function-like set
K145(y2,K174((((n * P) + (x1 * L1)) + (x2 * L2)))) is V16() Function-like set
(- x2) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((- n) * P) + ((- x1) * L1)) + ((- x2) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((((- n) * P) + ((- x1) * L1)) + ((- x2) * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
- (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K38(1) * (n * P) is V16() Function-like set
- (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K38(1) * (x1 * L1) is V16() Function-like set
(- (n * P)) + (- (x1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
- (x2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K38(1) * (x2 * L2) is V16() Function-like set
((- (n * P)) + (- (x1 * L1))) + (- (x2 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + (((- (n * P)) + (- (x1 * L1))) + (- (x2 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((- n) * P) + (- (x1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((- n) * P) + (- (x1 * L1))) + (- (x2 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((((- n) * P) + (- (x1 * L1))) + (- (x2 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((- n) * P) + ((- x1) * L1)) + (- (x2 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((((- n) * P) + ((- x1) * L1)) + (- (x2 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is V11() real ext-real Element of REAL
- n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n + x1 is V11() real ext-real Element of REAL
- x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(n + x1) + x2 is V11() real ext-real Element of REAL
- x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n + x1) + x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 - (((n + x1) + x2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((((n + x1) + x2) * P)) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (((n + x1) + x2) * P) is V16() Function-like set
K145(y2,K174((((n + x1) + x2) * P))) is V16() Function-like set
(- n) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((- n) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(- x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + ((- n) * P)) + ((- x1) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(- x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((y2 + ((- n) * P)) + ((- x1) * P)) + ((- x2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n + x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n + x1) * P) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 - (((n + x1) * P) + (x2 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((((n + x1) * P) + (x2 * P))) is V16() Function-like complex-yielding set
K38(1) * (((n + x1) * P) + (x2 * P)) is V16() Function-like set
K145(y2,K174((((n + x1) * P) + (x2 * P)))) is V16() Function-like set
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * P) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * P) + (x1 * P)) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 - (((n * P) + (x1 * P)) + (x2 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((((n * P) + (x1 * P)) + (x2 * P))) is V16() Function-like complex-yielding set
K38(1) * (((n * P) + (x1 * P)) + (x2 * P)) is V16() Function-like set
K145(y2,K174((((n * P) + (x1 * P)) + (x2 * P)))) is V16() Function-like set
((- n) * P) + ((- x1) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((- n) * P) + ((- x1) * P)) + ((- x2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((((- n) * P) + ((- x1) * P)) + ((- x2) * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + (((- n) * P) + ((- x1) * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + (((- n) * P) + ((- x1) * P))) + ((- x2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + (y1 + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + y1) + (x2 + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + x2) + y1) + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + y1) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + y1) + x2) + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + y2) + (x2 + P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + P) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + x2) + y1) + ((y2 + P) + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + y2) + (x2 + P)) + (y1 + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + (y2 + P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + x2) + (y2 + P)) + (y1 + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) - (y1 + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((y1 + y2)) is V16() Function-like complex-yielding set
K38(1) * (y1 + y2) is V16() Function-like set
K145((x1 + x2),K174((y1 + y2))) is V16() Function-like set
x2 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) * y2 is V16() Function-like set
K145(x2,K174(y2)) is V16() Function-like set
(x1 - y1) + (x2 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x1 + x2),K174(y1)) is V16() Function-like set
((x1 + x2) - y1) - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 + x2) - y1),K174(y2)) is V16() Function-like set
- y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- y1) + (- y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + ((- y1) + (- y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(x1,K174(y2)) is V16() Function-like set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(x2,K174(P)) is V16() Function-like set
(x1 - y2) + (x2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + P) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + x2) + y1) - ((y2 + P) + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((y2 + P) + L1)) is V16() Function-like complex-yielding set
K38(1) * ((y2 + P) + L1) is V16() Function-like set
K145(((x1 + x2) + y1),K174(((y2 + P) + L1))) is V16() Function-like set
y1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(y1,K174(L1)) is V16() Function-like set
((x1 - y2) + (x2 - P)) + (y1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + x2) - (y2 + P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((y2 + P)) is V16() Function-like complex-yielding set
K38(1) * (y2 + P) is V16() Function-like set
K145((x1 + x2),K174((y2 + P))) is V16() Function-like set
((x1 + x2) - (y2 + P)) + (y1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * x2) + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(x2 + y1) + y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * ((x2 + y1) + y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((n * x2) + (n * y1)) + (n * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * (x2 + y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * (x2 + y1)) + (n * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n * x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
n * x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x1 * y2) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * ((x1 * y2) + (x2 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * x1) * y2) + ((n * x2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * (x1 * y2)) + (n * (x2 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * x1) * y2) + (n * (x2 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n * x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
n * x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
n * y1 is V11() real ext-real Element of REAL
y2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y2 is non empty FinSequence-membered FinSequenceSet of REAL
y2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y2 } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x1 * P) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * x2) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * x1) * P) + ((n * x2) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((x1 * P) + (x2 * L1)) + (y1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * (((x1 * P) + (x2 * L1)) + (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * y1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * x1) * P) + ((n * x2) * L1)) + ((n * y1) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * (x1 * P)) + (n * (x2 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * (y1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * (x1 * P)) + (n * (x2 * L1))) + (n * (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * x1) * P) + (n * (x2 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * x1) * P) + (n * (x2 * L1))) + (n * (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * x1) * P) + ((n * x2) * L1)) + (n * (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
n + x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
x1 + y1 is V11() real ext-real Element of REAL
y2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y2 is non empty FinSequence-membered FinSequenceSet of REAL
y2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y2 } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n + x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * P) + (y1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * P) + (x1 * L1)) + ((x2 * P) + (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x1 + y1) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n + x2) * P) + ((x1 + y1) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * P) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x1 * L1) + (y1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * P) + (x2 * P)) + ((x1 * L1) + (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n + x2) * P) + ((x1 * L1) + (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
n + y1 is V11() real ext-real Element of REAL
y2 is V11() real ext-real Element of REAL
x1 + y2 is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
x2 + P is V11() real ext-real Element of REAL
L1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL L1 is non empty FinSequence-membered FinSequenceSet of REAL
L1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = L1 } is set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
n * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(n + y1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(n * L2) + (x1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y1 * L2) + (y2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + y2) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n + y1) * L2) + ((x1 + y2) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x2 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n * L2) + (x1 * x1)) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
P * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((y1 * L2) + (y2 * x1)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n * L2) + (x1 * x1)) + (x2 * L)) + (((y1 * L2) + (y2 * x1)) + (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x2 + P) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n + y1) * L2) + ((x1 + y2) * x1)) + ((x2 + P) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n * L2) + (x1 * x1)) + ((y1 * L2) + (y2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x2 * L) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n * L2) + (x1 * x1)) + ((y1 * L2) + (y2 * x1))) + ((x2 * L) + (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n + y1) * L2) + ((x1 + y2) * x1)) + ((x2 * L) + (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
n - x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
x1 - y1 is V11() real ext-real Element of REAL
y2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y2 is non empty FinSequence-membered FinSequenceSet of REAL
y2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y2 } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n - x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * P) + (y1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * P) + (x1 * L1)) - ((x2 * P) + (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174(((x2 * P) + (y1 * L1))) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * ((x2 * P) + (y1 * L1)) is V16() Function-like set
K145(((n * P) + (x1 * L1)),K174(((x2 * P) + (y1 * L1)))) is V16() Function-like set
(x1 - y1) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n - x2) * P) + ((x1 - y1) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * P) - (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174((x2 * P)) is V16() Function-like complex-yielding set
K38(1) * (x2 * P) is V16() Function-like set
K145((n * P),K174((x2 * P))) is V16() Function-like set
(x1 * L1) - (y1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174((y1 * L1)) is V16() Function-like complex-yielding set
K38(1) * (y1 * L1) is V16() Function-like set
K145((x1 * L1),K174((y1 * L1))) is V16() Function-like set
((n * P) - (x2 * P)) + ((x1 * L1) - (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n - x2) * P) + ((x1 * L1) - (y1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
n - y1 is V11() real ext-real Element of REAL
y2 is V11() real ext-real Element of REAL
x1 - y2 is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
x2 - P is V11() real ext-real Element of REAL
L1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL L1 is non empty FinSequence-membered FinSequenceSet of REAL
L1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = L1 } is set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
n * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(n - y1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(n * L2) + (x1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y1 * L2) + (y2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 - y2) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n - y1) * L2) + ((x1 - y2) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x2 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n * L2) + (x1 * x1)) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
P * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((y1 * L2) + (y2 * x1)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n * L2) + (x1 * x1)) + (x2 * L)) - (((y1 * L2) + (y2 * x1)) + (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((((y1 * L2) + (y2 * x1)) + (P * L))) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (((y1 * L2) + (y2 * x1)) + (P * L)) is V16() Function-like set
K145((((n * L2) + (x1 * x1)) + (x2 * L)),K174((((y1 * L2) + (y2 * x1)) + (P * L)))) is V16() Function-like set
(x2 - P) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n - y1) * L2) + ((x1 - y2) * x1)) + ((x2 - P) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n * L2) + (x1 * x1)) - ((y1 * L2) + (y2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174(((y1 * L2) + (y2 * x1))) is V16() Function-like complex-yielding set
K38(1) * ((y1 * L2) + (y2 * x1)) is V16() Function-like set
K145(((n * L2) + (x1 * x1)),K174(((y1 * L2) + (y2 * x1)))) is V16() Function-like set
(x2 * L) - (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((P * L)) is V16() Function-like complex-yielding set
K38(1) * (P * L) is V16() Function-like set
K145((x2 * L),K174((P * L))) is V16() Function-like set
(((n * L2) + (x1 * x1)) - ((y1 * L2) + (y2 * x1))) + ((x2 * L) - (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((n - y1) * L2) + ((x1 - y2) * x1)) + ((x2 * L) - (P * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n + x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(n + x1) + x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * y2) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
x1 * (P - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + (x1 * (P - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * y2) + (x1 * P)) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K145(L1,K174(y2)) is V16() Function-like set
x2 * (L1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + (x1 * (P - y2))) + (x2 * (L1 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
1 - x1 is V11() real ext-real Element of REAL
(1 - x1) - x2 is V11() real ext-real Element of REAL
1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 * y2) - (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((x1 * y2)) is V16() Function-like complex-yielding set
K38(1) * (x1 * y2) is V16() Function-like set
K145((1 * y2),K174((x1 * y2))) is V16() Function-like set
x2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((1 * y2) - (x1 * y2)) - (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((x2 * y2)) is V16() Function-like complex-yielding set
K38(1) * (x2 * y2) is V16() Function-like set
K145(((1 * y2) - (x1 * y2)),K174((x2 * y2))) is V16() Function-like set
(((1 * y2) - (x1 * y2)) - (x2 * y2)) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((((1 * y2) - (x1 * y2)) - (x2 * y2)) + (x1 * P)) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
- (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + (- (x1 * y2))) - (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K145((y2 + (- (x1 * y2))),K174((x2 * y2))) is V16() Function-like set
((y2 + (- (x1 * y2))) - (x2 * y2)) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((y2 + (- (x1 * y2))) - (x2 * y2)) + (x1 * P)) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + (- (x1 * y2))) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
- (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((y2 + (- (x1 * y2))) + (x1 * P)) + (- (x2 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((y2 + (- (x1 * y2))) + (x1 * P)) + (- (x2 * y2))) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x1 * P) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y2 + ((x1 * P) + (- (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + ((x1 * P) + (- (x1 * y2)))) + (- (x2 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((y2 + ((x1 * P) + (- (x1 * y2)))) + (- (x2 * y2))) + (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x2 * L1) + (- (x2 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + ((x1 * P) + (- (x1 * y2)))) + ((x2 * L1) + (- (x2 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y2 + (x1 * (P - y2))) + ((x2 * L1) + (- (x2 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x2 is non empty FinSequence-membered FinSequenceSet of REAL
x2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x2 } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
n * (P - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
y2 + (n * (P - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
L1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K145(L1,K174(y2)) is V16() Function-like set
x1 * (L1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + (n * (P - y2))) + (x1 * (L1 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
1 - n is V11() real ext-real Element of REAL
(1 - n) - x1 is V11() real ext-real Element of REAL
L2 is V11() real ext-real Element of REAL
L2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(L2 * y2) + (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
((L2 * y2) + (n * P)) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
L2 + n is V11() real ext-real Element of REAL
(L2 + n) + x1 is V11() real ext-real Element of REAL
1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
n * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(1 * y2) - (n * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K174((n * y2)) is V16() Function-like complex-yielding set
K38(1) * (n * y2) is V16() Function-like set
K145((1 * y2),K174((n * y2))) is V16() Function-like set
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
((1 * y2) - (n * y2)) - (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K174((x1 * y2)) is V16() Function-like complex-yielding set
K38(1) * (x1 * y2) is V16() Function-like set
K145(((1 * y2) - (n * y2)),K174((x1 * y2))) is V16() Function-like set
(((1 * y2) - (n * y2)) - (x1 * y2)) + (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
((((1 * y2) - (n * y2)) - (x1 * y2)) + (n * P)) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
- (n * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
y2 + (- (n * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + (- (n * y2))) - (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
K145((y2 + (- (n * y2))),K174((x1 * y2))) is V16() Function-like set
((y2 + (- (n * y2))) - (x1 * y2)) + (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(((y2 + (- (n * y2))) - (x1 * y2)) + (n * P)) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + (- (n * y2))) + (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
- (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
((y2 + (- (n * y2))) + (n * P)) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(((y2 + (- (n * y2))) + (n * P)) + (- (x1 * y2))) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(n * P) + (- (n * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
y2 + ((n * P) + (- (n * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + ((n * P) + (- (n * y2)))) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
((y2 + ((n * P) + (- (n * y2)))) + (- (x1 * y2))) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(x1 * L1) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + ((n * P) + (- (n * y2)))) + ((x1 * L1) + (- (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
(y2 + (n * (P - y2))) + ((x1 * L1) + (- (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x2) FinSequence-like Element of REAL x2
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
1* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
n |-> 1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),1) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({1}) Function-like V30( Seg n,{1}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{1}:]
{1} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{1}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{1}:] is non empty set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(n |-> 0) . 1 is V11() real ext-real set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
x1 is Element of bool (REAL n)
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
P is V11() real ext-real Element of REAL
1 - P is V11() real ext-real Element of REAL
(1 - P) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - P) * y1) + (P * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V11() real ext-real Element of REAL
1 - L1 is V11() real ext-real Element of REAL
(1 - L1) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - L1) * y1) + (L1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - P is V11() real ext-real Element of REAL
(L1 - P) * (y2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 - L1) * y1) + (L1 * y2)) - ((1 - P) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((1 - P) * y1)) is V16() Function-like complex-yielding set
K38(1) * ((1 - P) * y1) is V16() Function-like set
K145((((1 - L1) * y1) + (L1 * y2)),K174(((1 - P) * y1))) is V16() Function-like set
((((1 - L1) * y1) + (L1 * y2)) - ((1 - P) * y1)) - (P * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((P * y2)) is V16() Function-like complex-yielding set
K38(1) * (P * y2) is V16() Function-like set
K145(((((1 - L1) * y1) + (L1 * y2)) - ((1 - P) * y1)),K174((P * y2))) is V16() Function-like set
(L1 * y2) + ((1 - L1) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (P * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 * y2) + ((1 - L1) * y1)) + (- (P * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((1 - P) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L1 * y2) + ((1 - L1) * y1)) + (- (P * y2))) + (- ((1 - P) * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 * y2) + (- (P * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 * y2) + (- (P * y2))) + ((1 - L1) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L1 * y2) + (- (P * y2))) + ((1 - L1) * y1)) + (- ((1 - P) * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 - P) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 - P) * y2) + ((1 - L1) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L1 - P) * y2) + ((1 - L1) * y1)) + (- ((1 - P) * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - L1) * y1) + (- ((1 - P) * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 - P) * y2) + (((1 - L1) * y1) + (- ((1 - P) * y1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 - L1) - (1 - P) is V11() real ext-real Element of REAL
((1 - L1) - (1 - P)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 - P) * y2) + (((1 - L1) - (1 - P)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (L1 - P) is V11() real ext-real Element of REAL
(- (L1 - P)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 - P) * y2) + ((- (L1 - P)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL * is FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
P is V11() real ext-real Element of REAL
P * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 / P is V11() real ext-real Element of REAL
(1 / P) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P / P is V11() real ext-real Element of REAL
(P / P) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V11() real ext-real Element of REAL
y2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V11() real ext-real Element of REAL
P * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P * y2 is V11() real ext-real Element of REAL
(P * y2) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
y2 is V11() real ext-real Element of REAL
y2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
{0} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V11() real ext-real Element of REAL
P * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V11() real ext-real Element of REAL
L1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P * y2) + (L1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + (0 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
y2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y2 is non empty FinSequence-membered FinSequenceSet of REAL
y2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y2 } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * P) + (y1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
0* y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y2 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of y2 -tuples_on REAL
Seg y2 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg y2),0) is V16() V19( Seg y2) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg y2,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg y2),{0}:]
[:(Seg y2),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg y2),{0}:] is non empty set
((n * P) + (x1 * L1)) - ((n * P) + (x1 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174(((n * P) + (x1 * L1))) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * ((n * P) + (x1 * L1)) is V16() Function-like set
K145(((n * P) + (x1 * L1)),K174(((n * P) + (x1 * L1)))) is V16() Function-like set
n - x2 is V11() real ext-real Element of REAL
(n - x2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 - y1 is V11() real ext-real Element of REAL
(x1 - y1) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n - x2) * P) + ((x1 - y1) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
y2 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y2 is non empty FinSequence-membered FinSequenceSet of REAL
y2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y2 } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * L1) + (x1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * L1) + (y1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x2 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K38(1) is V11() real ext-real non positive set
K38(1) * (x2 * L) is V16() Function-like set
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- (x2 * L)) + (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- x2 is V11() real ext-real Element of REAL
(- x2) * ((n * L1) + (x1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * ((x2 * L1) + (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((- x2) * ((n * L1) + (x1 * L2))) + (n * ((x2 * L1) + (y1 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- x2) * n is V11() real ext-real Element of REAL
((- x2) * n) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- x2) * x1 is V11() real ext-real Element of REAL
((- x2) * x1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((- x2) * n) * L1) + (((- x2) * x1) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((((- x2) * n) * L1) + (((- x2) * x1) * L2)) + (n * ((x2 * L1) + (y1 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * x2 is V11() real ext-real Element of REAL
- (n * x2) is V11() real ext-real Element of REAL
(- (n * x2)) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * x2 is V11() real ext-real Element of REAL
- (x1 * x2) is V11() real ext-real Element of REAL
(- (x1 * x2)) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((- (n * x2)) * L1) + ((- (x1 * x2)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * x2) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n * y1 is V11() real ext-real Element of REAL
(n * y1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * x2) * L1) + ((n * y1) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((- (n * x2)) * L1) + ((- (x1 * x2)) * L2)) + (((n * x2) * L1) + ((n * y1) * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- (n * x2)) + (n * x2) is V11() real ext-real Element of REAL
((- (n * x2)) + (n * x2)) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- (x1 * x2)) + (n * y1) is V11() real ext-real Element of REAL
((- (x1 * x2)) + (n * y1)) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((- (n * x2)) + (n * x2)) * L1) + (((- (x1 * x2)) + (n * y1)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
0* y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y2 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of y2 -tuples_on REAL
Seg y2 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg y2),0) is V16() V19( Seg y2) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg y2,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg y2),{0}:]
[:(Seg y2),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg y2),{0}:] is non empty set
(0* y2) + (((- (x1 * x2)) + (n * y1)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * y1) - (x1 * x2) is V11() real ext-real Element of REAL
((n * y1) - (x1 * x2)) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
y1 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(y1 * L) - (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174((x1 * P)) is V16() Function-like complex-yielding set
K38(1) * (x1 * P) is V16() Function-like set
K145((y1 * L),K174((x1 * P))) is V16() Function-like set
(n * y1) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * y1 is V11() real ext-real Element of REAL
(x1 * y1) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * y1) * L1) + ((x1 * y1) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
x1 * ((x2 * L1) + (y1 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * y1) * L1) + ((x1 * y1) * L2)) - (x1 * ((x2 * L1) + (y1 * L2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174((x1 * ((x2 * L1) + (y1 * L2)))) is V16() Function-like complex-yielding set
K38(1) * (x1 * ((x2 * L1) + (y1 * L2))) is V16() Function-like set
K145((((n * y1) * L1) + ((x1 * y1) * L2)),K174((x1 * ((x2 * L1) + (y1 * L2))))) is V16() Function-like set
(x1 * x2) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((x1 * x2) * L1) + ((x1 * y1) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * y1) * L1) + ((x1 * y1) * L2)) - (((x1 * x2) * L1) + ((x1 * y1) * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174((((x1 * x2) * L1) + ((x1 * y1) * L2))) is V16() Function-like complex-yielding set
K38(1) * (((x1 * x2) * L1) + ((x1 * y1) * L2)) is V16() Function-like set
K145((((n * y1) * L1) + ((x1 * y1) * L2)),K174((((x1 * x2) * L1) + ((x1 * y1) * L2)))) is V16() Function-like set
((n * y1) - (x1 * x2)) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x1 * y1) - (x1 * y1) is V11() real ext-real Element of REAL
((x1 * y1) - (x1 * y1)) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * y1) - (x1 * x2)) * L1) + (((x1 * y1) - (x1 * y1)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((n * y1) - (x1 * x2)) * L1) + (0* y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- x1 is V11() real ext-real Element of REAL
(- x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(y1 * L) + ((- x1) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
0 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
0 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * L1) + (0 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * L1) + (0* y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * L1) + (0* y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- n is V11() real ext-real Element of REAL
(- n) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(x2 * L) + ((- n) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- n) * (x2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * x2) * L1) + ((- n) * (x2 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- n) * x2 is V11() real ext-real Element of REAL
((- n) * x2) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((n * x2) * L1) + (((- n) * x2) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(n * x2) + ((- n) * x2) is V11() real ext-real Element of REAL
((n * x2) + ((- n) * x2)) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(0* y2) + (0 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(0* y2) + (0* y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
1 / ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
(1 / ((n * y1) - (x1 * x2))) * ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
((1 / ((n * y1) - (x1 * x2))) * ((n * y1) - (x1 * x2))) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (((n * y1) - (x1 * x2)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (- (x2 * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (n * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((1 / ((n * y1) - (x1 * x2))) * (- (x2 * L))) + ((1 / ((n * y1) - (x1 * x2))) * (n * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- x2) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * ((- x2) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((1 / ((n * y1) - (x1 * x2))) * ((- x2) * L)) + ((1 / ((n * y1) - (x1 * x2))) * (n * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(- x2) / ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
((- x2) / ((n * y1) - (x1 * x2))) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((- x2) / ((n * y1) - (x1 * x2))) * L) + ((1 / ((n * y1) - (x1 * x2))) * (n * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n / ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
(n / ((n * y1) - (x1 * x2))) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(((- x2) / ((n * y1) - (x1 * x2))) * L) + ((n / ((n * y1) - (x1 * x2))) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- x1 is V11() real ext-real Element of REAL
(- x1) / ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
y1 / ((n * y1) - (x1 * x2)) is V11() real ext-real Element of REAL
(y1 / ((n * y1) - (x1 * x2))) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((- x1) / ((n * y1) - (x1 * x2))) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((y1 / ((n * y1) - (x1 * x2))) * L) + (((- x1) / ((n * y1) - (x1 * x2))) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((1 / ((n * y1) - (x1 * x2))) * ((n * y1) - (x1 * x2))) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (((n * y1) - (x1 * x2)) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (y1 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((1 / ((n * y1) - (x1 * x2))) * (y1 * L)) - ((1 / ((n * y1) - (x1 * x2))) * (x1 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K174(((1 / ((n * y1) - (x1 * x2))) * (x1 * P))) is V16() Function-like complex-yielding set
K38(1) * ((1 / ((n * y1) - (x1 * x2))) * (x1 * P)) is V16() Function-like set
K145(((1 / ((n * y1) - (x1 * x2))) * (y1 * L)),K174(((1 / ((n * y1) - (x1 * x2))) * (x1 * P)))) is V16() Function-like set
((y1 / ((n * y1) - (x1 * x2))) * L) - ((1 / ((n * y1) - (x1 * x2))) * (x1 * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K145(((y1 / ((n * y1) - (x1 * x2))) * L),K174(((1 / ((n * y1) - (x1 * x2))) * (x1 * P)))) is V16() Function-like set
(1 / ((n * y1) - (x1 * x2))) * x1 is V11() real ext-real Element of REAL
((1 / ((n * y1) - (x1 * x2))) * x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- (((1 / ((n * y1) - (x1 * x2))) * x1) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
K38(1) * (((1 / ((n * y1) - (x1 * x2))) * x1) * P) is V16() Function-like set
((y1 / ((n * y1) - (x1 * x2))) * L) + (- (((1 / ((n * y1) - (x1 * x2))) * x1) * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
- ((1 / ((n * y1) - (x1 * x2))) * x1) is V11() real ext-real Element of REAL
(- ((1 / ((n * y1) - (x1 * x2))) * x1)) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((y1 / ((n * y1) - (x1 * x2))) * L) + ((- ((1 / ((n * y1) - (x1 * x2))) * x1)) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
(1 / ((n * y1) - (x1 * x2))) * (- x1) is V11() real ext-real Element of REAL
((1 / ((n * y1) - (x1 * x2))) * (- x1)) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
((y1 / ((n * y1) - (x1 * x2))) * L) + (((1 / ((n * y1) - (x1 * x2))) * (- x1)) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y2) FinSequence-like Element of REAL y2
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + ((- 1) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
1 * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
1 * (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y1,K174(x2)) is V16() Function-like set
n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
0* x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x1 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of x1 -tuples_on REAL
Seg x1 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg x1),0) is V16() V19( Seg x1) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg x1,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg x1),{0}:]
[:(Seg x1),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg x1),{0}:] is non empty set
y2 is V11() real ext-real Element of REAL
y2 * (x2 + (n * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
P is V11() real ext-real Element of REAL
P * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(y2 * (x2 + (n * y1))) + (P * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(1 * x2) + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 * ((1 * x2) + (n * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(y2 * ((1 * x2) + (n * y1))) + (P * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 * 1 is V11() real ext-real Element of REAL
(y2 * 1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 * n is V11() real ext-real Element of REAL
(y2 * n) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((y2 * 1) * x2) + ((y2 * n) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(((y2 * 1) * x2) + ((y2 * n) * y1)) + (P * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((y2 * n) * y1) + (P * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(y2 * x2) + (((y2 * n) * y1) + (P * y1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(y2 * n) + P is V11() real ext-real Element of REAL
((y2 * n) + P) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(y2 * x2) + (((y2 * n) + P) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
Line (x2,x1) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ (((1 - b₁) * x2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) * y2 is V16() Function-like set
K145(y1,K174(y2)) is V16() Function-like set
Line (y2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
L is V11() real ext-real Element of REAL
L * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
x9 * (y1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x2 is V11() real ext-real Element of REAL
x2 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
x1 * (x1 - L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 * (L1 - P)) + (x1 * (x1 - L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * L is V11() real ext-real Element of REAL
(x2 * L) * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (x9 * (y1 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 * L) * (x1 - x2)) + (x1 * (x9 * (y1 - y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x9 is V11() real ext-real Element of REAL
(x1 * x9) * (y1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 * L) * (x1 - x2)) + ((x1 * x9) * (y1 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x9) / x9 is V11() real ext-real Element of REAL
(x2 * L) / L is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x1,K174(x1)) is V16() Function-like set
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (y1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (y1 * x2) is V16() Function-like set
(1 * x1) + (- (y1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y1 is V11() real ext-real Element of REAL
(- y1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + ((- y1) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V11() real ext-real Element of REAL
y2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 * x1) + (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y2 is V11() real ext-real Element of REAL
(- y2) / y1 is V11() real ext-real Element of REAL
(0* n) - (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((y2 * x2)) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (y2 * x2) is V16() Function-like set
K145((0* n),K174((y2 * x2))) is V16() Function-like set
- (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 / y1 is V11() real ext-real Element of REAL
(y1 / y1) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 / y1 is V11() real ext-real Element of REAL
(1 / y1) * (y1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- y2) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 / y1) * ((- y2) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- y2) / y1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- y1 is V11() real ext-real Element of REAL
(- y1) / y2 is V11() real ext-real Element of REAL
(0* n) - (y1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((y1 * x1)) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (y1 * x1) is V16() Function-like set
K145((0* n),K174((y1 * x1))) is V16() Function-like set
- (y1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 / y2 is V11() real ext-real Element of REAL
(y2 / y2) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 / y2 is V11() real ext-real Element of REAL
(1 / y2) * (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- y1) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 / y2) * ((- y1) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- y1) / y2) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(y1,K174(x1)) is V16() Function-like set
|((x1 - x2),(y1 - x1))| is V11() real ext-real Element of REAL
|.(x1 - x2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - x2),(x1 - x2)) is V16() Function-like set
K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
|.(x1 - x2).| ^2 is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)) is V11() real ext-real Element of REAL
1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) is V11() real ext-real Element of REAL
(1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like complex-yielding set
K38(1) * (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() Function-like set
K145(y1,K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))) is V16() Function-like set
|((x1 - x2),(y1 - (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))))| is V11() real ext-real Element of REAL
- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) is V11() real ext-real Element of REAL
1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) is V11() real ext-real Element of REAL
(1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - ((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1)) is V16() Function-like complex-yielding set
K38(1) * ((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1) is V16() Function-like set
K145(y1,K174(((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1))) is V16() Function-like set
(y1 - ((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() Function-like complex-yielding set
K38(1) * ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() Function-like set
K145((y1 - ((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1)),K174(((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like set
|((x1 - x2),((y1 - ((1 + (- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))| is V11() real ext-real Element of REAL
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - ((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))) is V16() Function-like complex-yielding set
K38(1) * ((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) is V16() Function-like set
K145(y1,K174(((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)))) is V16() Function-like set
(y1 - ((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((y1 - ((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))),K174(((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like set
|((x1 - x2),((y1 - ((1 * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))| is V11() real ext-real Element of REAL
y1 - (1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((1 * x1)) is V16() Function-like complex-yielding set
K38(1) * (1 * x1) is V16() Function-like set
K145(y1,K174((1 * x1))) is V16() Function-like set
(y1 - (1 * x1)) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) is V16() Function-like complex-yielding set
K38(1) * ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) is V16() Function-like set
K145((y1 - (1 * x1)),K174(((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))) is V16() Function-like set
((y1 - (1 * x1)) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((y1 - (1 * x1)) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)),K174(((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like set
|((x1 - x2),(((y1 - (1 * x1)) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))| is V11() real ext-real Element of REAL
(y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((y1 - x1),K174(((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1))) is V16() Function-like set
((y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)),K174(((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like set
|((x1 - x2),(((y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1)) - ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))| is V11() real ext-real Element of REAL
((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like complex-yielding set
K38(1) * (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() Function-like set
K145((y1 - x1),K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))) is V16() Function-like set
|((x1 - x2),((y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))))| is V11() real ext-real Element of REAL
(- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2) is V16() Function-like set
((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2)))) is V16() Function-like complex-yielding set
K38(1) * (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2))) is V16() Function-like set
K145((y1 - x1),K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2))))) is V16() Function-like set
|((x1 - x2),((y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + (- ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x2)))))| is V11() real ext-real Element of REAL
- x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2)))) is V16() Function-like complex-yielding set
K38(1) * (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2))) is V16() Function-like set
K145((y1 - x1),K174((((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2))))) is V16() Function-like set
|((x1 - x2),((y1 - x1) - (((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (- x2)))))| is V11() real ext-real Element of REAL
(- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2))) is V16() Function-like complex-yielding set
K38(1) * ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2)) is V16() Function-like set
K145((y1 - x1),K174(((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2)))) is V16() Function-like set
|((x1 - x2),((y1 - x1) - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2))))| is V11() real ext-real Element of REAL
|((x1 - x2),((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2)))| is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| - |((x1 - x2),((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * (x1 - x2)))| is V11() real ext-real Element of REAL
|((x1 - x2),(x1 - x2))| is V11() real ext-real Element of REAL
(- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * |((x1 - x2),(x1 - x2))| is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| - ((- (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * |((x1 - x2),(x1 - x2))|) is V11() real ext-real Element of REAL
(- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * |((x1 - x2),(x1 - x2))| is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * |((x1 - x2),(x1 - x2))|) is V11() real ext-real Element of REAL
(- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * (|.(x1 - x2).| ^2)) is V11() real ext-real Element of REAL
- |((x1 - x2),(y1 - x1))| is V11() real ext-real Element of REAL
(- |((x1 - x2),(y1 - x1))|) / (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
((- |((x1 - x2),(y1 - x1))|) / (|.(x1 - x2).| ^2)) * (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| + (((- |((x1 - x2),(y1 - x1))|) / (|.(x1 - x2).| ^2)) * (|.(x1 - x2).| ^2)) is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| + (- |((x1 - x2),(y1 - x1))|) is V11() real ext-real Element of REAL
y2 is V11() real ext-real Element of REAL
1 - y2 is V11() real ext-real Element of REAL
(1 - y2) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - y2) * x1) + (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(y1,K174(L1)) is V16() Function-like set
|((x1 - x2),(y1 - L1))| is V11() real ext-real Element of REAL
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(y1,K174(x1)) is V16() Function-like set
|((x1 - x2),(y1 - x1))| is V11() real ext-real Element of REAL
|.(x1 - x2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - x2),(x1 - x2)) is V16() Function-like set
K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
|.(x1 - x2).| ^2 is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)) is V11() real ext-real Element of REAL
1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) is V11() real ext-real Element of REAL
(1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like complex-yielding set
K38(1) * (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() Function-like set
K145(y1,K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))) is V16() Function-like set
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(y1,K174(x1)) is V16() Function-like set
|((x1 - x2),(y1 - x1))| is V11() real ext-real Element of REAL
|.(x1 - x2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - x2),(x1 - x2)) is V16() Function-like set
K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - x2))) is V11() real ext-real Element of REAL
|.(x1 - x2).| ^2 is V11() real ext-real Element of REAL
|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2) is V11() real ext-real Element of REAL
- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)) is V11() real ext-real Element of REAL
1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) is V11() real ext-real Element of REAL
(1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2))) is V16() Function-like complex-yielding set
K38(1) * (((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)) is V16() Function-like set
K145(y1,K174((((1 - (- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2)))) * x1) + ((- (|((x1 - x2),(y1 - x1))| / (|.(x1 - x2).| ^2))) * x2)))) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V11() real ext-real Element of REAL
y2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|(x1,y1)| is V11() real ext-real Element of REAL
|(x1,x2)| is V11() real ext-real Element of REAL
y2 * |(x1,x2)| is V11() real ext-real Element of REAL
y2 * 0 is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|(x1,x2)| is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
|(x1,x1)| is V11() real ext-real Element of REAL
|(x2,x2)| is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
y1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V11() real ext-real Element of REAL
y2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 * x1) + (y2 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|(((y1 * x1) + (y2 * x2)),((y1 * x1) + (y2 * x2)))| is V11() real ext-real Element of REAL
|((y1 * x1),(y1 * x1))| is V11() real ext-real Element of REAL
|((y1 * x1),(y2 * x2))| is V11() real ext-real Element of REAL
2 * |((y1 * x1),(y2 * x2))| is V11() real ext-real Element of REAL
|((y1 * x1),(y1 * x1))| + (2 * |((y1 * x1),(y2 * x2))|) is V11() real ext-real Element of REAL
|((y2 * x2),(y2 * x2))| is V11() real ext-real Element of REAL
(|((y1 * x1),(y1 * x1))| + (2 * |((y1 * x1),(y2 * x2))|)) + |((y2 * x2),(y2 * x2))| is V11() real ext-real Element of REAL
|(x1,(y1 * x1))| is V11() real ext-real Element of REAL
y1 * |(x1,(y1 * x1))| is V11() real ext-real Element of REAL
(y1 * |(x1,(y1 * x1))|) + (2 * |((y1 * x1),(y2 * x2))|) is V11() real ext-real Element of REAL
((y1 * |(x1,(y1 * x1))|) + (2 * |((y1 * x1),(y2 * x2))|)) + |((y2 * x2),(y2 * x2))| is V11() real ext-real Element of REAL
|(x1,(y2 * x2))| is V11() real ext-real Element of REAL
y1 * |(x1,(y2 * x2))| is V11() real ext-real Element of REAL
2 * (y1 * |(x1,(y2 * x2))|) is V11() real ext-real Element of REAL
(y1 * |(x1,(y1 * x1))|) + (2 * (y1 * |(x1,(y2 * x2))|)) is V11() real ext-real Element of REAL
((y1 * |(x1,(y1 * x1))|) + (2 * (y1 * |(x1,(y2 * x2))|))) + |((y2 * x2),(y2 * x2))| is V11() real ext-real Element of REAL
2 * y1 is V11() real ext-real Element of REAL
(2 * y1) * |(x1,(y2 * x2))| is V11() real ext-real Element of REAL
(y1 * |(x1,(y1 * x1))|) + ((2 * y1) * |(x1,(y2 * x2))|) is V11() real ext-real Element of REAL
|(x2,(y2 * x2))| is V11() real ext-real Element of REAL
y2 * |(x2,(y2 * x2))| is V11() real ext-real Element of REAL
((y1 * |(x1,(y1 * x1))|) + ((2 * y1) * |(x1,(y2 * x2))|)) + (y2 * |(x2,(y2 * x2))|) is V11() real ext-real Element of REAL
y1 * |(x1,x1)| is V11() real ext-real Element of REAL
y1 * (y1 * |(x1,x1)|) is V11() real ext-real Element of REAL
(y1 * (y1 * |(x1,x1)|)) + ((2 * y1) * |(x1,(y2 * x2))|) is V11() real ext-real Element of REAL
((y1 * (y1 * |(x1,x1)|)) + ((2 * y1) * |(x1,(y2 * x2))|)) + (y2 * |(x2,(y2 * x2))|) is V11() real ext-real Element of REAL
y1 * y1 is V11() real ext-real Element of REAL
(y1 * y1) * |(x1,x1)| is V11() real ext-real Element of REAL
y2 * |(x1,x2)| is V11() real ext-real Element of REAL
(2 * y1) * (y2 * |(x1,x2)|) is V11() real ext-real Element of REAL
((y1 * y1) * |(x1,x1)|) + ((2 * y1) * (y2 * |(x1,x2)|)) is V11() real ext-real Element of REAL
(((y1 * y1) * |(x1,x1)|) + ((2 * y1) * (y2 * |(x1,x2)|))) + (y2 * |(x2,(y2 * x2))|) is V11() real ext-real Element of REAL
(2 * y1) * y2 is V11() real ext-real Element of REAL
((2 * y1) * y2) * |(x1,x2)| is V11() real ext-real Element of REAL
((y1 * y1) * |(x1,x1)|) + (((2 * y1) * y2) * |(x1,x2)|) is V11() real ext-real Element of REAL
y2 * |(x2,x2)| is V11() real ext-real Element of REAL
y2 * (y2 * |(x2,x2)|) is V11() real ext-real Element of REAL
(((y1 * y1) * |(x1,x1)|) + (((2 * y1) * y2) * |(x1,x2)|)) + (y2 * (y2 * |(x2,x2)|)) is V11() real ext-real Element of REAL
y2 * y2 is V11() real ext-real Element of REAL
(y2 * y2) * |(x2,x2)| is V11() real ext-real Element of REAL
((y1 * y1) * |(x1,x1)|) + ((y2 * y2) * |(x2,x2)|) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
|(x2,x2)| is V11() real ext-real Element of REAL
|(x1,x2)| is V11() real ext-real Element of REAL
y1 * |(x2,x2)| is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
bool (REAL n) is non empty set
bool (bool (REAL n)) is non empty set
x2 is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(n) is Element of bool (bool (REAL n))
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
1* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
K277((Seg n),1) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({1}) Function-like V30( Seg n,{1}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{1}:]
{1} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{1}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{1}:] is non empty set
Line ((0* n),(1* n)) is Element of bool (REAL n)
{ (((1 - b₁) * (0* n)) + (b₁ * (1* n))) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 is Element of bool (REAL n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x2 is Element of (n)
y1 is Element of (n)
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(y1,K174(y2)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(x1,K174(P)) is V16() Function-like set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L1,K174(P)) is V16() Function-like set
L2 is V11() real ext-real Element of REAL
L2 * (y1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y2,K174(y1)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in x2 } is set
y2 is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(x1,K174(P)) is V16() Function-like set
|.(x1 - P).| is V11() real ext-real non negative Element of REAL
sqr (x1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - P),(x1 - P)) is V16() Function-like set
K402((sqr (x1 - P))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - P))) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
(n,x1,x2) is V45() V46() V47() Element of bool REAL
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in x2 } is set
lower_bound (n,x1,x2) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
y2 is Element of (n)
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
{ |.(y1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in Line (x1,x2) } is set
(n,y1,y2) is V45() V46() V47() Element of bool REAL
{ |.(y1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in y2 } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
(n,x1,x2) is V11() real ext-real Element of REAL
(n,x1,x2) is V45() V46() V47() Element of bool REAL
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in x2 } is set
lower_bound (n,x1,x2) is V11() real ext-real Element of REAL
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in Line (y1,y2) } is set
P is V45() V46() V47() Element of bool REAL
lower_bound P is V11() real ext-real Element of REAL
y1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(y1,K174(y2)) is V16() Function-like set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(x1,K174(L1)) is V16() Function-like set
|.(x1 - L1).| is V11() real ext-real non negative Element of REAL
sqr (x1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - L1),(x1 - L1)) is V16() Function-like set
K402((sqr (x1 - L1))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - L1))) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
(n,x1,x2) is V11() real ext-real Element of REAL
(n,x1,x2) is V45() V46() V47() Element of bool REAL
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in x2 } is set
lower_bound (n,x1,x2) is V11() real ext-real Element of REAL
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
|.(x1 - y1).| is V11() real ext-real non negative Element of REAL
sqr (x1 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - y1),(x1 - y1)) is V16() Function-like set
K402((sqr (x1 - y1))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - y1))) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
(n,x1,x2) is V11() real ext-real Element of REAL
(n,x1,x2) is V45() V46() V47() Element of bool REAL
{ |.(x1 - b₁).| where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : b₁ in x2 } is set
lower_bound (n,x1,x2) is V11() real ext-real Element of REAL
y1 is V11() real ext-real set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(x1,K174(y2)) is V16() Function-like set
|.(x1 - y2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - y2),(x1 - y2)) is V16() Function-like set
K402((sqr (x1 - y2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - y2))) is V11() real ext-real Element of REAL
y1 is ext-real set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(x1,K174(y2)) is V16() Function-like set
|.(x1 - y2).| is V11() real ext-real non negative Element of REAL
sqr (x1 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - y2),(x1 - y2)) is V16() Function-like set
K402((sqr (x1 - y2))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - y2))) is V11() real ext-real Element of REAL
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x1,K174(x1)) is V16() Function-like set
|.(x1 - x1).| is empty V11() real ext-real non positive non negative V45() V46() V47() V48() V49() V50() V51() Element of REAL
sqr (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - x1),(x1 - x1)) is V16() Function-like set
K402((sqr (x1 - x1))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - x1))) is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
|.(0* n).| is V11() real ext-real non negative Element of REAL
sqr (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((0* n),(0* n)) is V16() Function-like set
K402((sqr (0* n))) is V11() real ext-real Element of REAL
sqrt K402((sqr (0* n))) is V11() real ext-real Element of REAL
|((0* n),(0* n))| is V11() real ext-real Element of REAL
sqrt |((0* n),(0* n))| is V11() real ext-real Element of REAL
y1 is V11() real ext-real set
0 + y1 is V11() real ext-real Element of REAL
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
|.(x1 - y1).| is V11() real ext-real non negative Element of REAL
sqr (x1 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like FinSequence of REAL
mlt ((x1 - y1),(x1 - y1)) is V16() Function-like set
K402((sqr (x1 - y1))) is V11() real ext-real Element of REAL
sqrt K402((sqr (x1 - y1))) is V11() real ext-real Element of REAL
|((x1 - y1),(x1 - y1))| is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
y1 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 is Element of (n)
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,L2) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
L2 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(L2,K174(L1)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,L) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x9,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x9) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(L,K174(x1)) is V16() Function-like set
x2 - x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x9) is V16() Function-like complex-yielding set
K38(1) * x9 is V16() Function-like set
K145(x2,K174(x9)) is V16() Function-like set
Line (L,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 is V11() real ext-real Element of REAL
x1 * (L - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
y1 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 is Element of (n)
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,L2) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
L2 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(L2,K174(L1)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,L) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x9,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x9) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(L,K174(x1)) is V16() Function-like set
x2 - x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x9) is V16() Function-like complex-yielding set
K38(1) * x9 is V16() Function-like set
K145(x2,K174(x9)) is V16() Function-like set
x1 is V11() real ext-real Element of REAL
x1 * (L - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(x1,K174(y1)) is V16() Function-like set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y2,K174(y1)) is V16() Function-like set
Line (y1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is Element of bool (REAL n)
L1 is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
1 * (y2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
bool (REAL x1) is non empty set
(x1) is non empty Element of bool (bool (REAL x1))
bool (bool (REAL x1)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1 : verum } is set
0* x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x1 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of x1 -tuples_on REAL
Seg x1 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg x1),0) is V16() V19( Seg x1) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg x1,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg x1),{0}:]
[:(Seg x1),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg x1),{0}:] is non empty set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is Element of (x1)
1 - n is V11() real ext-real Element of REAL
1 / (1 - n) is V11() real ext-real Element of REAL
1 - (1 / (1 - n)) is V11() real ext-real Element of REAL
(1 / (1 - n)) * n is V11() real ext-real Element of REAL
(1 - (1 / (1 - n))) + ((1 / (1 - n)) * n) is V11() real ext-real Element of REAL
n / (1 - n) is V11() real ext-real Element of REAL
(1 - (1 / (1 - n))) + (n / (1 - n)) is V11() real ext-real Element of REAL
- (1 / (1 - n)) is V11() real ext-real Element of REAL
(- (1 / (1 - n))) + (n / (1 - n)) is V11() real ext-real Element of REAL
1 + ((- (1 / (1 - n))) + (n / (1 - n))) is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive Element of REAL
(- 1) / (1 - n) is V11() real ext-real Element of REAL
((- 1) / (1 - n)) + (n / (1 - n)) is V11() real ext-real Element of REAL
1 + (((- 1) / (1 - n)) + (n / (1 - n))) is V11() real ext-real Element of REAL
(- 1) + n is V11() real ext-real Element of REAL
((- 1) + n) / (1 - n) is V11() real ext-real Element of REAL
1 + (((- 1) + n) / (1 - n)) is V11() real ext-real Element of REAL
- n is V11() real ext-real Element of REAL
(- n) + 1 is V11() real ext-real Element of REAL
- ((- n) + 1) is V11() real ext-real Element of REAL
(- ((- n) + 1)) / (1 - n) is V11() real ext-real Element of REAL
1 + ((- ((- n) + 1)) / (1 - n)) is V11() real ext-real Element of REAL
(1 - n) / (1 - n) is V11() real ext-real Element of REAL
- ((1 - n) / (1 - n)) is V11() real ext-real Element of REAL
1 + (- ((1 - n) / (1 - n))) is V11() real ext-real Element of REAL
1 - ((1 - n) / (1 - n)) is V11() real ext-real Element of REAL
1 - 1 is V11() real ext-real Element of REAL
0 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(1 - (1 / (1 - n))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((1 / (1 - n)) * n) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((1 - (1 / (1 - n))) * x2) + (((1 / (1 - n)) * n) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(1 / (1 - n)) * (n * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((1 - (1 / (1 - n))) * x2) + ((1 / (1 - n)) * (n * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
Line (x2,(n * x2)) is Element of bool (REAL x1)
{ (((1 - b₁) * x2) + (b₁ * (n * x2))) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is V11() real ext-real Element of REAL
x1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL x1 is non empty FinSequence-membered FinSequenceSet of REAL
x1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = x1 } is set
bool (REAL x1) is non empty set
(x1) is non empty Element of bool (bool (REAL x1))
bool (bool (REAL x1)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1 : verum } is set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(y1,K174(x2)) is V16() Function-like set
n * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
y2 is Element of (x1)
1 - n is V11() real ext-real Element of REAL
(1 - n) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((1 - n) * x2) + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
Line (x2,y1) is Element of bool (REAL x1)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
n * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
- (n * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K38(1) * (n * x2) is V16() Function-like set
(1 * x2) + (- (n * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
((1 * x2) + (- (n * x2))) + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 + (- (n * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(x2 + (- (n * x2))) + (n * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(n * y1) + (- (n * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 + ((n * y1) + (- (n * x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
x2 + (n * (y1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
(((1 - n) * x2) + (n * y1)) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(x1) FinSequence-like Element of REAL x1
K145((((1 - n) * x2) + (n * y1)),K174(x2)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y1,K174(x1)) is V16() Function-like set
y2 is Element of (n)
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V11() real ext-real Element of REAL
P * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) * y2 is V16() Function-like set
K145(L,K174(y2)) is V16() Function-like set
x9 is V11() real ext-real Element of REAL
x9 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x9,K174(y2)) is V16() Function-like set
x2 is V11() real ext-real Element of REAL
x2 * (x1 - L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,L) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * L)) where b₁ is V11() real ext-real Element of REAL : verum } is set
Line (y2,x9) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * x9)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x2 is set
x1 is V11() real ext-real Element of REAL
1 - x1 is V11() real ext-real Element of REAL
(1 - x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - x1) * y2) + (x1 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is V11() real ext-real Element of REAL
x * (x9 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x1 * y2) is V16() Function-like set
(1 * y2) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * y2) + (- (x1 * y2))) + (x1 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + (- (x1 * y2))) + (x1 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * L) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + ((x1 * L) + (- (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (L - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (x1 * (L - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x is V11() real ext-real Element of REAL
(x1 * x) * (x9 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + ((x1 * x) * (x9 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((x1 * x) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((x1 * x) * y2) is V16() Function-like set
((x1 * x) * x9) + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (((x1 * x) * x9) + (- ((x1 * x) * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + (- ((x1 * x) * y2))) + ((x1 * x) * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * y2) + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * y2) + (- ((x1 * x) * y2))) + ((x1 * x) * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 - (x1 * x) is V11() real ext-real Element of REAL
(1 - (x1 * x)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (x1 * x)) * y2) + ((x1 * x) * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is set
x1 is V11() real ext-real Element of REAL
1 - x1 is V11() real ext-real Element of REAL
(1 - x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - x1) * y2) + (x1 * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is V11() real ext-real Element of REAL
x * (L - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x1 * y2) is V16() Function-like set
(1 * y2) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * y2) + (- (x1 * y2))) + (x1 * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + (- (x1 * y2))) + (x1 * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x9) + (- (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + ((x1 * x9) + (- (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (x9 - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (x1 * (x9 - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x is V11() real ext-real Element of REAL
(x1 * x) * (L - y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + ((x1 * x) * (L - y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((x1 * x) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((x1 * x) * y2) is V16() Function-like set
((x1 * x) * L) + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (((x1 * x) * L) + (- ((x1 * x) * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y2 + (- ((x1 * x) * y2))) + ((x1 * x) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * y2) + (- ((x1 * x) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * y2) + (- ((x1 * x) * y2))) + ((x1 * x) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 - (x1 * x) is V11() real ext-real Element of REAL
(1 - (x1 * x)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (x1 * x)) * y2) + ((x1 * x) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
x1 + (y2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,(x1 + (y2 - y1))) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * (x1 + (y2 - y1)))) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 is Element of (n)
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(x1 + (y2 - y1)) - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145((x1 + (y2 - y1)),K174(x1)) is V16() Function-like set
1 * (y2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
P is Element of (n)
L1 is Element of (n)
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L,x9) is Element of bool (REAL n)
{ (((1 - b₁) * L) + (b₁ * x9)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
x9 - L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L) is V16() Function-like complex-yielding set
K38(1) * L is V16() Function-like set
K145(x9,K174(L)) is V16() Function-like set
x2 is V11() real ext-real Element of REAL
x2 * (x1 - L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x1 - L2),(x9 - L))| is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x1 * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x2 - x1),(y2 - y1))| is V11() real ext-real Element of REAL
|((x1 - L2),(y2 - y1))| is V11() real ext-real Element of REAL
x2 * |((x1 - L2),(y2 - y1))| is V11() real ext-real Element of REAL
x1 * |((x1 - L2),(x9 - L))| is V11() real ext-real Element of REAL
x2 * (x1 * |((x1 - L2),(x9 - L))|) is V11() real ext-real Element of REAL
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(y1)) is V16() Function-like set
L1 is V11() real ext-real Element of REAL
L1 * (P - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
L1 is V11() real ext-real Element of REAL
L1 * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
L1 * (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
P is Element of (n)
L1 is Element of (n)
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L,x9) is Element of bool (REAL n)
{ (((1 - b₁) * L) + (b₁ * x9)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L2) is V16() Function-like complex-yielding set
K38(1) * L2 is V16() Function-like set
K145(x1,K174(L2)) is V16() Function-like set
x9 - L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L) is V16() Function-like complex-yielding set
K38(1) * L is V16() Function-like set
K145(x9,K174(L)) is V16() Function-like set
x2 is V11() real ext-real Element of REAL
x2 * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is V11() real ext-real Element of REAL
x1 * (x1 - L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is V11() real ext-real Element of REAL
x * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x is V11() real ext-real Element of REAL
(x1 * x) * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * (1 * (x9 - L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 / x2 is V11() real ext-real Element of REAL
(1 / x2) * x2 is V11() real ext-real Element of REAL
((1 / x2) * x2) * (x9 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * (((1 / x2) * x2) * (x9 - L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 / x2) * (x2 * (x9 - L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * ((1 / x2) * (x2 * (x9 - L))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) * (1 / x2) is V11() real ext-real Element of REAL
((x1 * x) * (1 / x2)) * (x2 * (x9 - L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x) / x2 is V11() real ext-real Element of REAL
((x1 * x) / x2) * (y2 - y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x1,K174(x2)) is V16() Function-like set
Line (x2,x1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y1,K174(x2)) is V16() Function-like set
Line (x2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
Line (x1,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y2,K174(x2)) is V16() Function-like set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(x2)) is V16() Function-like set
L1 is Element of (n)
L2 is Element of (n)
x1 is V11() real ext-real Element of REAL
1 - x1 is V11() real ext-real Element of REAL
(1 - x1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - x1) * x2) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(y1,K174(x1)) is V16() Function-like set
L is V11() real ext-real Element of REAL
L * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
1 - x9 is V11() real ext-real Element of REAL
(1 - x9) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - x9) * x2) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(P - y2) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * (y1 - x1))) is V16() Function-like complex-yielding set
K38(1) * (L * (y1 - x1)) is V16() Function-like set
K145((P - y2),K174((L * (y1 - x1)))) is V16() Function-like set
(((1 - x1) * x2) + (x1 * y1)) - ((1 - x9) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((1 - x9) * x2)) is V16() Function-like complex-yielding set
K38(1) * ((1 - x9) * x2) is V16() Function-like set
K145((((1 - x1) * x2) + (x1 * y1)),K174(((1 - x9) * x2))) is V16() Function-like set
((((1 - x1) * x2) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x9 * x1)) is V16() Function-like complex-yielding set
K38(1) * (x9 * x1) is V16() Function-like set
K145(((((1 - x1) * x2) + (x1 * y1)) - ((1 - x9) * x2)),K174((x9 * x1))) is V16() Function-like set
(((((1 - x1) * x2) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 - x1) * x2) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x1 * x2) is V16() Function-like set
(1 * x2) + (- (x1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x2) + (- (x1 * x2))) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 - x9) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((1 * x2) + (- (x1 * x2))) + (x1 * y1)),K174(((1 - x9) * x2))) is V16() Function-like set
((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 - x9) * x2)),K174((x9 * x1))) is V16() Function-like set
(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 - x9) * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
x9 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x9 * x2) is V16() Function-like set
(1 * x2) + (- (x9 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 * x2) + (- (x9 * x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((1 * x2) + (- (x9 * x2)))) is V16() Function-like complex-yielding set
K38(1) * ((1 * x2) + (- (x9 * x2))) is V16() Function-like set
K145((((1 * x2) + (- (x1 * x2))) + (x1 * y1)),K174(((1 * x2) + (- (x9 * x2))))) is V16() Function-like set
((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 * x2) + (- (x9 * x2)))) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 * x2) + (- (x9 * x2)))),K174((x9 * x1))) is V16() Function-like set
(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 * x2) + (- (x9 * x2)))) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - ((1 * x2) + (- (x9 * x2)))) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
(((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((1 * x2)) is V16() Function-like complex-yielding set
K38(1) * (1 * x2) is V16() Function-like set
K145((((1 * x2) + (- (x1 * x2))) + (x1 * y1)),K174((1 * x2))) is V16() Function-like set
((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)) - (- (x9 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((- (x9 * x2))) is V16() Function-like complex-yielding set
K38(1) * (- (x9 * x2)) is V16() Function-like set
K145(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)),K174((- (x9 * x2)))) is V16() Function-like set
(((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)) - (- (x9 * x2))) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)) - (- (x9 * x2))),K174((x9 * x1))) is V16() Function-like set
((((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)) - (- (x9 * x2))) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((((1 * x2) + (- (x1 * x2))) + (x1 * y1)) - (1 * x2)) - (- (x9 * x2))) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
- (1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x2) + (- (x1 * x2))) + (- (1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1)) + (x9 * x2)),K174((x9 * x1))) is V16() Function-like set
((((((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((((1 * x2) + (- (x1 * x2))) + (- (1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
(1 * x2) + (- (1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x2) + (- (1 * x2))) + (- (x1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)),K174((x9 * x1))) is V16() Function-like set
((((((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((((1 * x2) + (- (1 * x2))) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
(0* n) + (- (x1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + (- (x1 * x2))) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((0* n) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((0* n) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((0* n) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)),K174((x9 * x1))) is V16() Function-like set
(((((0* n) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((((0* n) + (- (x1 * x2))) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
(- (x1 * x2)) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (x1 * x2)) + (x1 * y1)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((- (x1 * x2)) + (x1 * y1)) + (x9 * x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((- (x1 * x2)) + (x1 * y1)) + (x9 * x2)),K174((x9 * x1))) is V16() Function-like set
((((- (x1 * x2)) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((((- (x1 * x2)) + (x1 * y1)) + (x9 * x2)) - (x9 * x1)),K174((L * (y1 - x1)))) is V16() Function-like set
x1 * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * (y1 - x2)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) + (x9 * x2)) + (- (x9 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 * (y1 - x2)) + (x9 * x2)) + (- (x9 * x1))) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((x1 * (y1 - x2)) + (x9 * x2)) + (- (x9 * x1))),K174((L * (y1 - x1)))) is V16() Function-like set
(x1 * (y1 - x2)) - (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x1 * (y1 - x2)),K174((x9 * x1))) is V16() Function-like set
((x1 * (y1 - x2)) - (x9 * x1)) + (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 * (y1 - x2)) - (x9 * x1)) + (x9 * x2)) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((x1 * (y1 - x2)) - (x9 * x1)) + (x9 * x2)),K174((L * (y1 - x1)))) is V16() Function-like set
(x9 * x1) - (x9 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x9 * x2)) is V16() Function-like complex-yielding set
K145((x9 * x1),K174((x9 * x2))) is V16() Function-like set
(x1 * (y1 - x2)) - ((x9 * x1) - (x9 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((x9 * x1) - (x9 * x2))) is V16() Function-like complex-yielding set
K38(1) * ((x9 * x1) - (x9 * x2)) is V16() Function-like set
K145((x1 * (y1 - x2)),K174(((x9 * x1) - (x9 * x2)))) is V16() Function-like set
((x1 * (y1 - x2)) - ((x9 * x1) - (x9 * x2))) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 * (y1 - x2)) - ((x9 * x1) - (x9 * x2))),K174((L * (y1 - x1)))) is V16() Function-like set
x9 * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * (y1 - x2)) - (x9 * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x9 * (x1 - x2))) is V16() Function-like complex-yielding set
K38(1) * (x9 * (x1 - x2)) is V16() Function-like set
K145((x1 * (y1 - x2)),K174((x9 * (x1 - x2)))) is V16() Function-like set
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * (y1 - x1)))) is V16() Function-like set
y1 - (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((0* n)) is V16() Function-like complex-yielding set
K38(1) * (0* n) is V16() Function-like set
K145(y1,K174((0* n))) is V16() Function-like set
(y1 - (0* n)) - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((y1 - (0* n)),K174(x1)) is V16() Function-like set
L * ((y1 - (0* n)) - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * ((y1 - (0* n)) - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * ((y1 - (0* n)) - x1))) is V16() Function-like complex-yielding set
K38(1) * (L * ((y1 - (0* n)) - x1)) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * ((y1 - (0* n)) - x1)))) is V16() Function-like set
x2 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x2,K174(x2)) is V16() Function-like set
y1 - (x2 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x2 - x2)) is V16() Function-like complex-yielding set
K38(1) * (x2 - x2) is V16() Function-like set
K145(y1,K174((x2 - x2))) is V16() Function-like set
(y1 - (x2 - x2)) - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((y1 - (x2 - x2)),K174(x1)) is V16() Function-like set
L * ((y1 - (x2 - x2)) - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * ((y1 - (x2 - x2)) - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * ((y1 - (x2 - x2)) - x1))) is V16() Function-like complex-yielding set
K38(1) * (L * ((y1 - (x2 - x2)) - x1)) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * ((y1 - (x2 - x2)) - x1)))) is V16() Function-like set
(y1 - x2) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((y1 - x2) + x2) + (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (((y1 - x2) + x2) + (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * (((y1 - x2) + x2) + (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * (((y1 - x2) + x2) + (- x1)))) is V16() Function-like complex-yielding set
K38(1) * (L * (((y1 - x2) + x2) + (- x1))) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * (((y1 - x2) + x2) + (- x1))))) is V16() Function-like set
(- x1) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(y1 - x2) + ((- x1) + x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * ((y1 - x2) + ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * ((y1 - x2) + ((- x1) + x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * ((y1 - x2) + ((- x1) + x2)))) is V16() Function-like complex-yielding set
K38(1) * (L * ((y1 - x2) + ((- x1) + x2))) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * ((y1 - x2) + ((- x1) + x2))))) is V16() Function-like set
L * ((- x1) + x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * (y1 - x2)) + (L * ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - ((L * (y1 - x2)) + (L * ((- x1) + x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((L * (y1 - x2)) + (L * ((- x1) + x2)))) is V16() Function-like complex-yielding set
K38(1) * ((L * (y1 - x2)) + (L * ((- x1) + x2))) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174(((L * (y1 - x2)) + (L * ((- x1) + x2))))) is V16() Function-like set
((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * (y1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * (y1 - x2))) is V16() Function-like complex-yielding set
K38(1) * (L * (y1 - x2)) is V16() Function-like set
K145(((x1 * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * (y1 - x2)))) is V16() Function-like set
(((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * (y1 - x2))) - (L * ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * ((- x1) + x2))) is V16() Function-like complex-yielding set
K38(1) * (L * ((- x1) + x2)) is V16() Function-like set
K145((((x1 * (y1 - x2)) - (x9 * (x1 - x2))) - (L * (y1 - x2))),K174((L * ((- x1) + x2)))) is V16() Function-like set
(L * (y1 - x2)) + (x9 * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * (y1 - x2)) - ((L * (y1 - x2)) + (x9 * (x1 - x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((L * (y1 - x2)) + (x9 * (x1 - x2)))) is V16() Function-like complex-yielding set
K38(1) * ((L * (y1 - x2)) + (x9 * (x1 - x2))) is V16() Function-like set
K145((x1 * (y1 - x2)),K174(((L * (y1 - x2)) + (x9 * (x1 - x2))))) is V16() Function-like set
((x1 * (y1 - x2)) - ((L * (y1 - x2)) + (x9 * (x1 - x2)))) - (L * ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 * (y1 - x2)) - ((L * (y1 - x2)) + (x9 * (x1 - x2)))),K174((L * ((- x1) + x2)))) is V16() Function-like set
(x1 * (y1 - x2)) - (L * (y1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x1 * (y1 - x2)),K174((L * (y1 - x2)))) is V16() Function-like set
((x1 * (y1 - x2)) - (L * (y1 - x2))) - (x9 * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 * (y1 - x2)) - (L * (y1 - x2))),K174((x9 * (x1 - x2)))) is V16() Function-like set
(((x1 * (y1 - x2)) - (L * (y1 - x2))) - (x9 * (x1 - x2))) - (L * ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((x1 * (y1 - x2)) - (L * (y1 - x2))) - (x9 * (x1 - x2))),K174((L * ((- x1) + x2)))) is V16() Function-like set
x1 - L is V11() real ext-real Element of REAL
(x1 - L) * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 - L) * (y1 - x2)),K174((x9 * (x1 - x2)))) is V16() Function-like set
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - (L * ((- x1) + x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))),K174((L * ((- x1) + x2)))) is V16() Function-like set
L * (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * (- x1)) + (L * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - ((L * (- x1)) + (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((L * (- x1)) + (L * x2))) is V16() Function-like complex-yielding set
K38(1) * ((L * (- x1)) + (L * x2)) is V16() Function-like set
K145((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))),K174(((L * (- x1)) + (L * x2)))) is V16() Function-like set
L * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (L * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (L * x1) is V16() Function-like set
(- (L * x1)) + (L * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - ((- (L * x1)) + (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((- (L * x1)) + (L * x2))) is V16() Function-like complex-yielding set
K38(1) * ((- (L * x1)) + (L * x2)) is V16() Function-like set
K145((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))),K174(((- (L * x1)) + (L * x2)))) is V16() Function-like set
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - (- (L * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((- (L * x1))) is V16() Function-like complex-yielding set
K38(1) * (- (L * x1)) is V16() Function-like set
K145((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))),K174((- (L * x1)))) is V16() Function-like set
((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - (- (L * x1))) - (L * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * x2)) is V16() Function-like complex-yielding set
K38(1) * (L * x2) is V16() Function-like set
K145(((((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) - (- (L * x1))),K174((L * x2))) is V16() Function-like set
- (L * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * x1) + (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) + ((L * x1) + (- (L * x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 - L) * (y1 - x2)) - (x9 * (x1 - x2))) + (L * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (x1 - x2)) - (L * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * (x1 - x2))) is V16() Function-like complex-yielding set
K38(1) * (L * (x1 - x2)) is V16() Function-like set
K145((x9 * (x1 - x2)),K174((L * (x1 - x2)))) is V16() Function-like set
((x1 - L) * (y1 - x2)) - ((x9 * (x1 - x2)) - (L * (x1 - x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((x9 * (x1 - x2)) - (L * (x1 - x2)))) is V16() Function-like complex-yielding set
K38(1) * ((x9 * (x1 - x2)) - (L * (x1 - x2))) is V16() Function-like set
K145(((x1 - L) * (y1 - x2)),K174(((x9 * (x1 - x2)) - (L * (x1 - x2))))) is V16() Function-like set
x9 - L is V11() real ext-real Element of REAL
(x9 - L) * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((x9 - L) * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((x9 - L) * (x1 - x2)) is V16() Function-like set
((x1 - L) * (y1 - x2)) + (- ((x9 - L) * (x1 - x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x9 - L) is V11() real ext-real Element of REAL
(- (x9 - L)) * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 - L) * (y1 - x2)) + ((- (x9 - L)) * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L - x9 is V11() real ext-real Element of REAL
(L - x9) * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 - L) * (y1 - x2)) + ((L - x9) * (x1 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x2) + (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x2) + (- (L * x2))) + (L * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (L * x2))) + (L * y1)) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((1 * x2) + (- (L * x2))) + (L * y1)),K174(x2)) is V16() Function-like set
x2 + (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 + (- (L * x2))) + (L * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 + (- (L * x2))) + (L * y1)) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x2 + (- (L * x2))) + (L * y1)),K174(x2)) is V16() Function-like set
(- (L * x2)) + (L * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (L * x2)) + (L * y1)) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((- (L * x2)) + (L * y1)) + x2) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((- (L * x2)) + (L * y1)) + x2),K174(x2)) is V16() Function-like set
((- (L * x2)) + (L * y1)) + (x2 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (L * x2)) + (L * y1)) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x2) + (- (L * x2))) + (L * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 * x2) + (- (L * x2))) + (L * x1)) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((1 * x2) + (- (L * x2))) + (L * x1)),K174(x2)) is V16() Function-like set
(x2 + (- (L * x2))) + (L * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 + (- (L * x2))) + (L * x1)) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x2 + (- (L * x2))) + (L * x1)),K174(x2)) is V16() Function-like set
(- (L * x2)) + (L * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (L * x2)) + (L * x1)) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((- (L * x2)) + (L * x1)) + x2) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((((- (L * x2)) + (L * x1)) + x2),K174(x2)) is V16() Function-like set
((- (L * x2)) + (L * x1)) + (x2 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- (L * x2)) + (L * x1)) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
x1 * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
x1 * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x9) is V16() Function-like complex-yielding set
K38(1) * x9 is V16() Function-like set
K145(x2,K174(x9)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(x,K174(x1)) is V16() Function-like set
x2 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x2,K174(x2)) is V16() Function-like set
L is V11() real ext-real Element of REAL
L * (x2 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (L * (x2 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 + (L * (x2 - x2))) - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x2 + (L * (x2 - x2))),K174(x1)) is V16() Function-like set
(L * (x2 - x2)) + x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x9,K174(x2)) is V16() Function-like set
L * (x9 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * (x2 - x2)) + x2) - (x2 + (L * (x9 - x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x2 + (L * (x9 - x2)))) is V16() Function-like complex-yielding set
K38(1) * (x2 + (L * (x9 - x2))) is V16() Function-like set
K145(((L * (x2 - x2)) + x2),K174((x2 + (L * (x9 - x2))))) is V16() Function-like set
((L * (x2 - x2)) + x2) - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * (x2 - x2)) + x2),K174(x2)) is V16() Function-like set
(((L * (x2 - x2)) + x2) - x2) - (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * (x9 - x2))) is V16() Function-like complex-yielding set
K38(1) * (L * (x9 - x2)) is V16() Function-like set
K145((((L * (x2 - x2)) + x2) - x2),K174((L * (x9 - x2)))) is V16() Function-like set
x2 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x2,K174(x2)) is V16() Function-like set
(L * (x2 - x2)) + (x2 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * (x2 - x2)) + (x2 - x2)) - (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * (x2 - x2)) + (x2 - x2)),K174((L * (x9 - x2)))) is V16() Function-like set
(L * (x2 - x2)) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * (x2 - x2)) + (0* n)) - (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * (x2 - x2)) + (0* n)),K174((L * (x9 - x2)))) is V16() Function-like set
(L * (x2 - x2)) - (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((L * (x2 - x2)),K174((L * (x9 - x2)))) is V16() Function-like set
L * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (L * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (L * x2) is V16() Function-like set
(L * x2) + (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x2) + (- (L * x2))) - (L * (x9 - x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * x2) + (- (L * x2))),K174((L * (x9 - x2)))) is V16() Function-like set
L * x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (L * x2)) + (L * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x2) + (- (L * x2))) - ((- (L * x2)) + (L * x9)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((- (L * x2)) + (L * x9))) is V16() Function-like complex-yielding set
K38(1) * ((- (L * x2)) + (L * x9)) is V16() Function-like set
K145(((L * x2) + (- (L * x2))),K174(((- (L * x2)) + (L * x9)))) is V16() Function-like set
((L * x2) + (- (L * x2))) - (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((- (L * x2))) is V16() Function-like complex-yielding set
K38(1) * (- (L * x2)) is V16() Function-like set
K145(((L * x2) + (- (L * x2))),K174((- (L * x2)))) is V16() Function-like set
(((L * x2) + (- (L * x2))) - (- (L * x2))) - (L * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L * x9)) is V16() Function-like complex-yielding set
K38(1) * (L * x9) is V16() Function-like set
K145((((L * x2) + (- (L * x2))) - (- (L * x2))),K174((L * x9))) is V16() Function-like set
(- (L * x2)) - (- (L * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((- (L * x2)),K174((- (L * x2)))) is V16() Function-like set
(L * x2) + ((- (L * x2)) - (- (L * x2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x2) + ((- (L * x2)) - (- (L * x2)))) - (L * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * x2) + ((- (L * x2)) - (- (L * x2)))),K174((L * x9))) is V16() Function-like set
(L * x2) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x2) + (0* n)) - (L * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((L * x2) + (0* n)),K174((L * x9))) is V16() Function-like set
(L * x2) - (L * x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((L * x2),K174((L * x9))) is V16() Function-like set
L * (x2 - x9) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
x1 * (x1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (y1 - x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
bool (REAL n) is non empty set
P is set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
L2 + x1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
(L2 + x1) + L is V11() real ext-real Element of REAL
L2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L2 * x1) + (x1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L2 * x1) + (x1 * x2)) + (L * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,x2,y1) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
0 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
1 + 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 + 0) + 0 is non empty V11() real ext-real positive non negative Element of REAL
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + (0 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x1) + (0 * x2)) + (0 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,x2,y1) is non empty Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
0 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + (0 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x1) + (0 * x2)) + (0 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0 * x1) + (0 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0 * x1) + (0 * x2)) + (1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0 * x1) + (1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0 * x1) + (1 * x2)) + (0 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0 + 0 is empty V11() real ext-real non positive non negative V45() V46() V47() V48() V49() V50() V51() Element of REAL
(0 + 0) + 1 is non empty V11() real ext-real positive non negative Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x2,y1,y2) is non empty Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x2) + (b₃ * y1)) + (b₄ * y2) ) } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,P,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * P)) + (b₄ * L1) ) } is set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
x1 + L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
(x1 + L) + x9 is V11() real ext-real Element of REAL
x1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * x2) + (L * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * x2) + (L * y1)) + (x9 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
L2 + x1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
(L2 + x1) + L is V11() real ext-real Element of REAL
L2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L2 * x2) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L2 * x2) + (x1 * y1)) + (L * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 + x1 is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
(x2 + x1) + x is V11() real ext-real Element of REAL
x2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 * x2) + (x1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 * x2) + (x1 * y1)) + (x * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x9 + x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(x9 + x2) + x1 is V11() real ext-real Element of REAL
x9 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * x2) + (x2 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * x2) + (x2 * y1)) + (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is set
b is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 is V11() real ext-real Element of REAL
a33 is V11() real ext-real Element of REAL
a32 + a33 is V11() real ext-real Element of REAL
c1 is V11() real ext-real Element of REAL
(a32 + a33) + c1 is V11() real ext-real Element of REAL
a32 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * x1) + (a33 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((a32 * x1) + (a33 * P)) + (c1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b is V11() real ext-real Element of REAL
a32 is V11() real ext-real Element of REAL
b + a32 is V11() real ext-real Element of REAL
a33 is V11() real ext-real Element of REAL
(b + a32) + a33 is V11() real ext-real Element of REAL
b * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b * x1) + (a32 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * x1) + (a32 * P)) + (a33 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c2 is V11() real ext-real Element of REAL
d1 is V11() real ext-real Element of REAL
c2 + d1 is V11() real ext-real Element of REAL
d2 is V11() real ext-real Element of REAL
(c2 + d1) + d2 is V11() real ext-real Element of REAL
c2 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
d1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(c2 * x2) + (d1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
d2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((c2 * x2) + (d1 * y1)) + (d2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c1 is V11() real ext-real Element of REAL
c2 is V11() real ext-real Element of REAL
c1 + c2 is V11() real ext-real Element of REAL
d1 is V11() real ext-real Element of REAL
(c1 + c2) + d1 is V11() real ext-real Element of REAL
c1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(c1 * x2) + (c2 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
d1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((c1 * x2) + (c2 * y1)) + (d1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b * x9 is V11() real ext-real Element of REAL
a32 * L2 is V11() real ext-real Element of REAL
(b * x9) + (a32 * L2) is V11() real ext-real Element of REAL
a33 * c1 is V11() real ext-real Element of REAL
((b * x9) + (a32 * L2)) + (a33 * c1) is V11() real ext-real Element of REAL
b * x2 is V11() real ext-real Element of REAL
a32 * x1 is V11() real ext-real Element of REAL
(b * x2) + (a32 * x1) is V11() real ext-real Element of REAL
a33 * c2 is V11() real ext-real Element of REAL
((b * x2) + (a32 * x1)) + (a33 * c2) is V11() real ext-real Element of REAL
(((b * x9) + (a32 * L2)) + (a33 * c1)) + (((b * x2) + (a32 * x1)) + (a33 * c2)) is V11() real ext-real Element of REAL
b * x1 is V11() real ext-real Element of REAL
a32 * L is V11() real ext-real Element of REAL
(b * x1) + (a32 * L) is V11() real ext-real Element of REAL
a33 * d1 is V11() real ext-real Element of REAL
((b * x1) + (a32 * L)) + (a33 * d1) is V11() real ext-real Element of REAL
((((b * x9) + (a32 * L2)) + (a33 * c1)) + (((b * x2) + (a32 * x1)) + (a33 * c2))) + (((b * x1) + (a32 * L)) + (a33 * d1)) is V11() real ext-real Element of REAL
b * ((x9 + x2) + x1) is V11() real ext-real Element of REAL
a32 * ((L2 + x1) + L) is V11() real ext-real Element of REAL
(b * ((x9 + x2) + x1)) + (a32 * ((L2 + x1) + L)) is V11() real ext-real Element of REAL
a33 * ((c1 + c2) + d1) is V11() real ext-real Element of REAL
((b * ((x9 + x2) + x1)) + (a32 * ((L2 + x1) + L))) + (a33 * ((c1 + c2) + d1)) is V11() real ext-real Element of REAL
(b * x9) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b * x2) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * x9) * x2) + ((b * x2) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b * x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 * (((L2 * x2) + (x1 * y1)) + (L * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2)) + (a32 * (((L2 * x2) + (x1 * y1)) + (L * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 * (((c1 * x2) + (c2 * y1)) + (d1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2)) + (a32 * (((L2 * x2) + (x1 * y1)) + (L * y2)))) + (a33 * (((c1 * x2) + (c2 * y1)) + (d1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * L2) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * x1) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((a32 * L2) * x2) + ((a32 * x1) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * L) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((a32 * L2) * x2) + ((a32 * x1) * y1)) + ((a32 * L) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2)) + ((((a32 * L2) * x2) + ((a32 * x1) * y1)) + ((a32 * L) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2)) + ((((a32 * L2) * x2) + ((a32 * x1) * y1)) + ((a32 * L) * y2))) + (a33 * (((c1 * x2) + (c2 * y1)) + (d1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a33 * c1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a33 * c2) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((a33 * c1) * x2) + ((a33 * c2) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a33 * d1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((a33 * c1) * x2) + ((a33 * c2) * y1)) + ((a33 * d1) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((b * x9) * x2) + ((b * x2) * y1)) + ((b * x1) * y2)) + ((((a32 * L2) * x2) + ((a32 * x1) * y1)) + ((a32 * L) * y2))) + ((((a33 * c1) * x2) + ((a33 * c2) * y1)) + ((a33 * d1) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * x9) + (a32 * L2)) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * x2) + (a32 * x1)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b * x9) + (a32 * L2)) * x2) + (((b * x2) + (a32 * x1)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * x1) + (a32 * L)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((b * x9) + (a32 * L2)) * x2) + (((b * x2) + (a32 * x1)) * y1)) + (((b * x1) + (a32 * L)) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((b * x9) + (a32 * L2)) * x2) + (((b * x2) + (a32 * x1)) * y1)) + (((b * x1) + (a32 * L)) * y2)) + ((((a33 * c1) * x2) + ((a33 * c2) * y1)) + ((a33 * d1) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b * x9) + (a32 * L2)) + (a33 * c1)) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b * x2) + (a32 * x1)) + (a33 * c2)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((b * x9) + (a32 * L2)) + (a33 * c1)) * x2) + ((((b * x2) + (a32 * x1)) + (a33 * c2)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b * x1) + (a32 * L)) + (a33 * d1)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((b * x9) + (a32 * L2)) + (a33 * c1)) * x2) + ((((b * x2) + (a32 * x1)) + (a33 * c2)) * y1)) + ((((b * x1) + (a32 * L)) + (a33 * d1)) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,y1,y2,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * y2)) + (b₄ * P) ) } is set
L1 is V11() real ext-real Element of REAL
L2 is V11() real ext-real Element of REAL
L1 + L2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(L1 + L2) + x1 is V11() real ext-real Element of REAL
L1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 * y1) + (L2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 * y1) + (L2 * y2)) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V11() real ext-real Element of REAL
L2 is V11() real ext-real Element of REAL
L1 + L2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(L1 + L2) + x1 is V11() real ext-real Element of REAL
L1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 * y1) + (L2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 * y1) + (L2 * y2)) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x9 + x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(x9 + x2) + x1 is V11() real ext-real Element of REAL
x9 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * y1) + (x2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * y1) + (x2 * y2)) + (x1 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
L + x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(L + x9) + x2 is V11() real ext-real Element of REAL
L * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * y1) + (x9 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * y1) + (x9 * y2)) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- L1 is V11() real ext-real Element of REAL
L + (- L1) is V11() real ext-real Element of REAL
- L2 is V11() real ext-real Element of REAL
x9 + (- L2) is V11() real ext-real Element of REAL
(L + (- L1)) + (x9 + (- L2)) is V11() real ext-real Element of REAL
- x1 is V11() real ext-real Element of REAL
x2 + (- x1) is V11() real ext-real Element of REAL
((L + (- L1)) + (x9 + (- L2))) + (x2 + (- x1)) is V11() real ext-real Element of REAL
x2 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x2 is V16() Function-like set
K145(x2,K174(x2)) is V16() Function-like set
(- L1) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- L2) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- L1) * y1) + ((- L2) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((- L1) * y1) + ((- L2) * y2)) + ((- x1) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L * y1) + (x9 * y2)) + (x2 * P)) + ((((- L1) * y1) + ((- L2) * y2)) + ((- x1) * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L + (- L1)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 + (- L2)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L + (- L1)) * y1) + ((x9 + (- L2)) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 + (- x1)) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L + (- L1)) * y1) + ((x9 + (- L2)) * y2)) + ((x2 + (- x1)) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x2,y1,y2) is non empty Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x2) + (b₃ * y1)) + (b₄ * y2) ) } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,P) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is set
L is V11() real ext-real Element of REAL
1 - L is V11() real ext-real Element of REAL
(1 - L) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - L) * x1) + (L * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x9 + x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(x9 + x2) + x1 is V11() real ext-real Element of REAL
x9 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * x2) + (x2 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * x2) + (x2 * y1)) + (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
x9 + x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(x9 + x2) + x1 is V11() real ext-real Element of REAL
x9 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * x2) + (x2 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * x2) + (x2 * y1)) + (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is V11() real ext-real Element of REAL
b is V11() real ext-real Element of REAL
x + b is V11() real ext-real Element of REAL
a32 is V11() real ext-real Element of REAL
(x + b) + a32 is V11() real ext-real Element of REAL
x * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x * x2) + (b * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x * x2) + (b * y1)) + (a32 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x is V11() real ext-real Element of REAL
b is V11() real ext-real Element of REAL
x + b is V11() real ext-real Element of REAL
a32 is V11() real ext-real Element of REAL
(x + b) + a32 is V11() real ext-real Element of REAL
x * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x * x2) + (b * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x * x2) + (b * y1)) + (a32 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 - L) * x is V11() real ext-real Element of REAL
L * x9 is V11() real ext-real Element of REAL
((1 - L) * x) + (L * x9) is V11() real ext-real Element of REAL
(1 - L) * b is V11() real ext-real Element of REAL
L * x2 is V11() real ext-real Element of REAL
((1 - L) * b) + (L * x2) is V11() real ext-real Element of REAL
(((1 - L) * x) + (L * x9)) + (((1 - L) * b) + (L * x2)) is V11() real ext-real Element of REAL
(1 - L) * a32 is V11() real ext-real Element of REAL
L * x1 is V11() real ext-real Element of REAL
((1 - L) * a32) + (L * x1) is V11() real ext-real Element of REAL
((((1 - L) * x) + (L * x9)) + (((1 - L) * b) + (L * x2))) + (((1 - L) * a32) + (L * x1)) is V11() real ext-real Element of REAL
(1 - L) * ((x + b) + a32) is V11() real ext-real Element of REAL
L * ((x9 + x2) + x1) is V11() real ext-real Element of REAL
((1 - L) * ((x + b) + a32)) + (L * ((x9 + x2) + x1)) is V11() real ext-real Element of REAL
(1 - L) + L is V11() real ext-real Element of REAL
((1 - L) * x) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - L) * b) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 - L) * x) * x2) + (((1 - L) * b) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - L) * a32) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((1 - L) * x) * x2) + (((1 - L) * b) * y1)) + (((1 - L) * a32) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (((x9 * x2) + (x2 * y1)) + (x1 * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((1 - L) * x) * x2) + (((1 - L) * b) * y1)) + (((1 - L) * a32) * y2)) + (L * (((x9 * x2) + (x2 * y1)) + (x1 * y2))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * x9) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * x2) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x9) * x2) + ((L * x2) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * x1) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((L * x9) * x2) + ((L * x2) * y1)) + ((L * x1) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((1 - L) * x) * x2) + (((1 - L) * b) * y1)) + (((1 - L) * a32) * y2)) + ((((L * x9) * x2) + ((L * x2) * y1)) + ((L * x1) * y2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 - L) * x) + (L * x9)) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 - L) * b) + (L * x2)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((((1 - L) * x) + (L * x9)) * x2) + ((((1 - L) * b) + (L * x2)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((1 - L) * a32) + (L * x1)) * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((((1 - L) * x) + (L * x9)) * x2) + ((((1 - L) * b) + (L * x2)) * y1)) + ((((1 - L) * a32) + (L * x1)) * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 is Element of bool (REAL n)
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V11() real ext-real Element of REAL
y1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 - y1 is V11() real ext-real Element of REAL
1 / (1 - y1) is V11() real ext-real Element of REAL
1 - (1 / (1 - y1)) is V11() real ext-real Element of REAL
(1 / (1 - y1)) * y1 is V11() real ext-real Element of REAL
(1 - (1 / (1 - y1))) + ((1 / (1 - y1)) * y1) is V11() real ext-real Element of REAL
y1 / (1 - y1) is V11() real ext-real Element of REAL
(1 - (1 / (1 - y1))) + (y1 / (1 - y1)) is V11() real ext-real Element of REAL
- (1 / (1 - y1)) is V11() real ext-real Element of REAL
(- (1 / (1 - y1))) + (y1 / (1 - y1)) is V11() real ext-real Element of REAL
1 + ((- (1 / (1 - y1))) + (y1 / (1 - y1))) is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive Element of REAL
(- 1) / (1 - y1) is V11() real ext-real Element of REAL
((- 1) / (1 - y1)) + (y1 / (1 - y1)) is V11() real ext-real Element of REAL
1 + (((- 1) / (1 - y1)) + (y1 / (1 - y1))) is V11() real ext-real Element of REAL
(- 1) + y1 is V11() real ext-real Element of REAL
((- 1) + y1) / (1 - y1) is V11() real ext-real Element of REAL
1 + (((- 1) + y1) / (1 - y1)) is V11() real ext-real Element of REAL
- y1 is V11() real ext-real Element of REAL
(- y1) - (- 1) is V11() real ext-real Element of REAL
- ((- y1) - (- 1)) is V11() real ext-real Element of REAL
(- ((- y1) - (- 1))) / (1 - y1) is V11() real ext-real Element of REAL
1 + ((- ((- y1) - (- 1))) / (1 - y1)) is V11() real ext-real Element of REAL
(1 - y1) / (1 - y1) is V11() real ext-real Element of REAL
- ((1 - y1) / (1 - y1)) is V11() real ext-real Element of REAL
1 + (- ((1 - y1) / (1 - y1))) is V11() real ext-real Element of REAL
1 - ((1 - y1) / (1 - y1)) is V11() real ext-real Element of REAL
1 - 1 is V11() real ext-real Element of REAL
0 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 - (1 / (1 - y1))) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 / (1 - y1)) * y1) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (1 / (1 - y1))) * x2) + (((1 / (1 - y1)) * y1) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 / (1 - y1)) * (y1 * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (1 / (1 - y1))) * x2) + ((1 / (1 - y1)) * (y1 * x2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x2,(y1 * x2)) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * (y1 * x2))) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(P,K174(y2)) is V16() Function-like set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L1,K174(y2)) is V16() Function-like set
(n,y2,P,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y2) + (b₃ * P)) + (b₄ * L1) ) } is set
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n + x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(n + x1) + x2 is V11() real ext-real Element of REAL
y1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL y1 is non empty FinSequence-membered FinSequenceSet of REAL
y1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = y1 } is set
0* y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
y1 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of y1 -tuples_on REAL
Seg y1 is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg y1),0) is V16() V19( Seg y1) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg y1,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg y1),{0}:]
[:(Seg y1),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg y1),{0}:] is non empty set
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(n * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(y1,P,L1,L2) is non empty Element of bool (REAL y1)
bool (REAL y1) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1 : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * P) + (b₃ * L1)) + (b₄ * L2) ) } is set
x2 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n * P) + (x1 * L1)) + (x2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
L + x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(L + x9) + x2 is V11() real ext-real Element of REAL
L * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x9 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(L * P) + (x9 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x2 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((L * P) + (x9 * L1)) + (x2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
x1 + L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
(x1 + L) + x9 is V11() real ext-real Element of REAL
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
L * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x1 * P) + (L * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
x9 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((x1 * P) + (L * L1)) + (x9 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n - x1 is V11() real ext-real Element of REAL
x1 - L is V11() real ext-real Element of REAL
(n - x1) + (x1 - L) is V11() real ext-real Element of REAL
x2 - x9 is V11() real ext-real Element of REAL
((n - x1) + (x1 - L)) + (x2 - x9) is V11() real ext-real Element of REAL
(n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9)) is V11() real ext-real Element of REAL
(x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9)) is V11() real ext-real Element of REAL
((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) + ((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9))) is V11() real ext-real Element of REAL
(x2 - x9) / (((n - x1) + (x1 - L)) + (x2 - x9)) is V11() real ext-real Element of REAL
(((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) + ((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9)))) + ((x2 - x9) / (((n - x1) + (x1 - L)) + (x2 - x9))) is V11() real ext-real Element of REAL
(((n - x1) + (x1 - L)) + (x2 - x9)) / (((n - x1) + (x1 - L)) + (x2 - x9)) is V11() real ext-real Element of REAL
(((n * P) + (x1 * L1)) + (x2 * L2)) - (((x1 * P) + (L * L1)) + (x9 * L2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
K174((((x1 * P) + (L * L1)) + (x9 * L2))) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * (((x1 * P) + (L * L1)) + (x9 * L2)) is V16() Function-like set
K145((((n * P) + (x1 * L1)) + (x2 * L2)),K174((((x1 * P) + (L * L1)) + (x9 * L2)))) is V16() Function-like set
(n - x1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x1 - L) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n - x1) * P) + ((x1 - L) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(x2 - x9) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((n - x1) * P) + ((x1 - L) * L1)) + ((x2 - x9) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
1 / (((n - x1) + (x1 - L)) + (x2 - x9)) is V11() real ext-real Element of REAL
(1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (0* y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (n - x1) is V11() real ext-real Element of REAL
((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (n - x1)) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L) is V11() real ext-real Element of REAL
((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L)) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (n - x1)) * P) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L)) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x2 - x9) is V11() real ext-real Element of REAL
((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x2 - x9)) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (n - x1)) * P) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L)) * L1)) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x2 - x9)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L)) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x1 - L)) * L1)) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x2 - x9)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
(((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P) + (((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P) + (((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L1)) + (((1 / (((n - x1) + (x1 - L)) + (x2 - x9))) * (x2 - x9)) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((x2 - x9) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
((((n - x1) / (((n - x1) + (x1 - L)) + (x2 - x9))) * P) + (((x1 - L) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L1)) + (((x2 - x9) / (((n - x1) + (x1 - L)) + (x2 - x9))) * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(y1) FinSequence-like Element of REAL y1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x2,y1,y2) is non empty Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x2) + (b₃ * y1)) + (b₄ * y2) ) } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V11() real ext-real Element of REAL
L2 is V11() real ext-real Element of REAL
L1 + L2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
(L1 + L2) + x1 is V11() real ext-real Element of REAL
L1 * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 * x2) + (L2 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L1 * x2) + (L2 * y1)) + (x1 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V11() real ext-real Element of REAL
L1 is V11() real ext-real Element of REAL
P + L1 is V11() real ext-real Element of REAL
L2 is V11() real ext-real Element of REAL
(P + L1) + L2 is V11() real ext-real Element of REAL
P * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P * x2) + (L1 * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 * y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P * x2) + (L1 * y1)) + (L2 * y2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
n + x1 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(n + x1) + x2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
y2 is V11() real ext-real Element of REAL
y1 + y2 is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
(y1 + y2) + P is V11() real ext-real Element of REAL
L1 is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL L1 is non empty FinSequence-membered FinSequenceSet of REAL
L1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = L1 } is set
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(L2,K174(x1)) is V16() Function-like set
n * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(n * x1) + (x1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y1 * x1) + (y2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K145(L,K174(x1)) is V16() Function-like set
x2 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((n * x1) + (x1 * L2)) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
P * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((y1 * x1) + (y2 * L2)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
1 - x1 is V11() real ext-real Element of REAL
(1 - x1) - x2 is V11() real ext-real Element of REAL
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(1 * x1) - (x1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((x1 * x1)) is V16() Function-like complex-yielding set
K38(1) * (x1 * x1) is V16() Function-like set
K145((1 * x1),K174((x1 * x1))) is V16() Function-like set
x2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((1 * x1) - (x1 * x1)) - (x2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((x2 * x1)) is V16() Function-like complex-yielding set
K38(1) * (x2 * x1) is V16() Function-like set
K145(((1 * x1) - (x1 * x1)),K174((x2 * x1))) is V16() Function-like set
(((1 * x1) - (x1 * x1)) - (x2 * x1)) + (x1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((((1 * x1) - (x1 * x1)) - (x2 * x1)) + (x1 * L2)) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
- (x1 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (- (x1 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (- (x1 * x1))) - (x2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K145((x1 + (- (x1 * x1))),K174((x2 * x1))) is V16() Function-like set
((x1 + (- (x1 * x1))) - (x2 * x1)) + (x1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((x1 + (- (x1 * x1))) - (x2 * x1)) + (x1 * L2)) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (- (x1 * x1))) + (x1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
- (x2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((x1 + (- (x1 * x1))) + (x1 * L2)) + (- (x2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((x1 + (- (x1 * x1))) + (x1 * L2)) + (- (x2 * x1))) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 * L2) + (- (x1 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + ((x1 * L2) + (- (x1 * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((x1 * L2) + (- (x1 * x1)))) + (- (x2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((x1 + ((x1 * L2) + (- (x1 * x1)))) + (- (x2 * x1))) + (x2 * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x2 * L) + (- (x2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((x1 * L2) + (- (x1 * x1)))) + ((x2 * L) + (- (x2 * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 * L2) + (x1 * (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + ((x1 * L2) + (x1 * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((x1 * L2) + (x1 * (- x1)))) + ((x2 * L) + (- (x2 * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x2 * (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x2 * L) + (x2 * (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((x1 * L2) + (x1 * (- x1)))) + ((x2 * L) + (x2 * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
L2 + (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * (L2 + (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (x1 * (L2 + (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (x1 * (L2 + (- x1)))) + ((x2 * L) + (x2 * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 * (L2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (x1 * (L2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x2 * (L - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (x1 * (L2 - x1))) + (x2 * (L - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x9 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K145(x9,K174(x1)) is V16() Function-like set
(x1 * (L2 - x1)) + (x2 * (L - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
1 - y2 is V11() real ext-real Element of REAL
(1 - y2) - P is V11() real ext-real Element of REAL
((1 - y2) - P) * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((1 - y2) - P) * x1) + (y2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((((1 - y2) - P) * x1) + (y2 * L2)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(1 * x1) - (y2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((y2 * x1)) is V16() Function-like complex-yielding set
K38(1) * (y2 * x1) is V16() Function-like set
K145((1 * x1),K174((y2 * x1))) is V16() Function-like set
P * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((1 * x1) - (y2 * x1)) - (P * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K174((P * x1)) is V16() Function-like complex-yielding set
K38(1) * (P * x1) is V16() Function-like set
K145(((1 * x1) - (y2 * x1)),K174((P * x1))) is V16() Function-like set
(((1 * x1) - (y2 * x1)) - (P * x1)) + (y2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((((1 * x1) - (y2 * x1)) - (P * x1)) + (y2 * L2)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
- (y2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (- (y2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (- (y2 * x1))) - (P * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
K145((x1 + (- (y2 * x1))),K174((P * x1))) is V16() Function-like set
((x1 + (- (y2 * x1))) - (P * x1)) + (y2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((x1 + (- (y2 * x1))) - (P * x1)) + (y2 * L2)) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (- (y2 * x1))) + (y2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
- (P * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((x1 + (- (y2 * x1))) + (y2 * L2)) + (- (P * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(((x1 + (- (y2 * x1))) + (y2 * L2)) + (- (P * x1))) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y2 * L2) + (- (y2 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + ((y2 * L2) + (- (y2 * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((y2 * L2) + (- (y2 * x1)))) + (- (P * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
((x1 + ((y2 * L2) + (- (y2 * x1)))) + (- (P * x1))) + (P * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(P * L) + (- (P * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((y2 * L2) + (- (y2 * x1)))) + ((P * L) + (- (P * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y2 * L2) + (y2 * (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + ((y2 * L2) + (y2 * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((y2 * L2) + (y2 * (- x1)))) + ((P * L) + (- (P * x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
P * (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(P * L) + (P * (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + ((y2 * L2) + (y2 * (- x1)))) + ((P * L) + (P * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * (L2 + (- x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (y2 * (L2 + (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (y2 * (L2 + (- x1)))) + ((P * L) + (P * (- x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
y2 * (L2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
x1 + (y2 * (L2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
P * (L - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(x1 + (y2 * (L2 - x1))) + (P * (L - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
(y2 * (L2 - x1)) + (P * (L - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(L1) FinSequence-like Element of REAL L1
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
bool (bool (REAL n)) is non empty set
x2 is set
y1 is Element of bool (REAL n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,y2,P,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y2) + (b₃ * P)) + (b₄ * L1) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
(n) is Element of bool (bool (REAL n))
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
1* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
K277((Seg n),1) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({1}) Function-like V30( Seg n,{1}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{1}:]
{1} is non empty V45() V46() V47() V48() V49() V50() set
[:(Seg n),{1}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{1}:] is non empty set
(n,(0* n),(1* n),(1* n)) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * (0* n)) + (b₃ * (1* n))) + (b₄ * (1* n)) ) } is set
x1 is Element of bool (REAL n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,x2,y1) is non empty Element of bool (REAL n)
bool (REAL n) is non empty set
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,x2,y1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
y2 is Element of (n)
P is Element of bool (REAL n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,L1,L2,x1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * L1) + (b₃ * L2)) + (b₄ * x1) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(y1,K174(x1)) is V16() Function-like set
(n,x1,x2,y1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
y2 is Element of (n)
P is Element of bool (REAL n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,L1,L2,x1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * L1) + (b₃ * L2)) + (b₄ * x1) ) } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,P,L1,L2) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * P) + (b₃ * L1)) + (b₄ * L2) ) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
L + x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(L + x9) + x2 is V11() real ext-real Element of REAL
L * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * P) + (x9 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * P) + (x9 * L1)) + (x2 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
x1 + L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
(x1 + L) + x9 is V11() real ext-real Element of REAL
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * P) + (L * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * P) + (L * L1)) + (x9 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
x1 + x is V11() real ext-real Element of REAL
b is V11() real ext-real Element of REAL
(x1 + x) + b is V11() real ext-real Element of REAL
x1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * P) + (x * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 * P) + (x * L1)) + (b * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
x2 + x1 is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
(x2 + x1) + x is V11() real ext-real Element of REAL
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 * P) + (x1 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 * P) + (x1 * L1)) + (x * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 is V11() real ext-real Element of REAL
a33 is V11() real ext-real Element of REAL
a32 + a33 is V11() real ext-real Element of REAL
c1 is V11() real ext-real Element of REAL
(a32 + a33) + c1 is V11() real ext-real Element of REAL
a32 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * P) + (a33 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c1 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((a32 * P) + (a33 * L1)) + (c1 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b is V11() real ext-real Element of REAL
a32 is V11() real ext-real Element of REAL
b + a32 is V11() real ext-real Element of REAL
a33 is V11() real ext-real Element of REAL
(b + a32) + a33 is V11() real ext-real Element of REAL
b * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b * P) + (a32 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b * P) + (a32 * L1)) + (a33 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
a32 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (a32 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L2,K174(P)) is V16() Function-like set
a33 * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (a32 * (L1 - P))) + (a33 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (x1 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (x1 * (L1 - P))) + (x * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((P + (x1 * (L1 - P))) + (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((P + (x1 * (L1 - P))) + (x * (L2 - P))) is V16() Function-like set
((P + (a32 * (L1 - P))) + (a33 * (L2 - P))) + (- ((P + (x1 * (L1 - P))) + (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x1 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x1 * (L1 - P)) is V16() Function-like set
(- P) + (- (x1 * (L1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x * (L2 - P)) is V16() Function-like set
((- P) + (- (x1 * (L1 - P)))) + (- (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P + (a32 * (L1 - P))) + (a33 * (L2 - P))) + (((- P) + (- (x1 * (L1 - P)))) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (- P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a32 * (L1 - P)) + (- (x1 * (L1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (- P)) + ((a32 * (L1 - P)) + (- (x1 * (L1 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(a33 * (L2 - P)) + (- (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P + (- P)) + ((a32 * (L1 - P)) + (- (x1 * (L1 - P))))) + ((a33 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(0* n) + ((a32 * (L1 - P)) + (- (x1 * (L1 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((a32 * (L1 - P)) + (- (x1 * (L1 - P))))) + ((a33 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a32 - x1 is V11() real ext-real Element of REAL
(a32 - x1) * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + ((a32 - x1) * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((a32 - x1) * (L1 - P))) + ((a33 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
a33 - x is V11() real ext-real Element of REAL
(a33 - x) * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((a32 - x1) * (L1 - P))) + ((a33 - x) * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((a32 - x1) * (L1 - P)) + ((a33 - x) * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (L * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (L * (L1 - P))) + (x9 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P + (L * (L1 - P))) + (x9 * (L2 - P))) + (- ((P + (x1 * (L1 - P))) + (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P + (L * (L1 - P))) + (x9 * (L2 - P))) + (((- P) + (- (x1 * (L1 - P)))) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * (L1 - P)) + (- (x1 * (L1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (- P)) + ((L * (L1 - P)) + (- (x1 * (L1 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (L2 - P)) + (- (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((P + (- P)) + ((L * (L1 - P)) + (- (x1 * (L1 - P))))) + ((x9 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + ((L * (L1 - P)) + (- (x1 * (L1 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((L * (L1 - P)) + (- (x1 * (L1 - P))))) + ((x9 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L - x1 is V11() real ext-real Element of REAL
(L - x1) * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + ((L - x1) * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((L - x1) * (L1 - P))) + ((x9 * (L2 - P)) + (- (x * (L2 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 - x is V11() real ext-real Element of REAL
(x9 - x) * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((0* n) + ((L - x1) * (L1 - P))) + ((x9 - x) * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L - x1) * (L1 - P)) + ((x9 - x) * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c1 is V11() real ext-real Element of REAL
c1 * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c2 is V11() real ext-real Element of REAL
c2 * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(c1 * (x2 - x1)) + (c2 * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
d1 is V11() real ext-real Element of REAL
d1 * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
d2 is V11() real ext-real Element of REAL
d2 * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(d1 * (x2 - x1)) + (d2 * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 * (L1 - P)) + (x * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + ((x1 * (L1 - P)) + (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y is set
b1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b2 is V11() real ext-real Element of REAL
b3 is V11() real ext-real Element of REAL
b2 + b3 is V11() real ext-real Element of REAL
c₂₆ is V11() real ext-real Element of REAL
(b2 + b3) + c₂₆ is V11() real ext-real Element of REAL
b2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b3 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b2 * P) + (b3 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c₂₆ * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b2 * P) + (b3 * L1)) + (c₂₆ * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b1 is V11() real ext-real Element of REAL
b2 is V11() real ext-real Element of REAL
b1 + b2 is V11() real ext-real Element of REAL
b3 is V11() real ext-real Element of REAL
(b1 + b2) + b3 is V11() real ext-real Element of REAL
b1 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b2 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b1 * P) + (b2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b3 * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b1 * P) + (b2 * L1)) + (b3 * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b2 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (b2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b3 * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (b2 * (L1 - P))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - ((x1 * (L1 - P)) + (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((x1 * (L1 - P)) + (x * (L2 - P)))) is V16() Function-like complex-yielding set
K38(1) * ((x1 * (L1 - P)) + (x * (L2 - P))) is V16() Function-like set
K145(x1,K174(((x1 * (L1 - P)) + (x * (L2 - P))))) is V16() Function-like set
(x1 - ((x1 * (L1 - P)) + (x * (L2 - P)))) + (b2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 - ((x1 * (L1 - P)) + (x * (L2 - P)))) + (b2 * (L1 - P))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - (x1 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x1 * (L1 - P))) is V16() Function-like complex-yielding set
K145(x1,K174((x1 * (L1 - P)))) is V16() Function-like set
(x1 - (x1 * (L1 - P))) - (x * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x * (L2 - P))) is V16() Function-like complex-yielding set
K145((x1 - (x1 * (L1 - P))),K174((x * (L2 - P)))) is V16() Function-like set
((x1 - (x1 * (L1 - P))) - (x * (L2 - P))) + (b2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 - (x1 * (L1 - P))) - (x * (L2 - P))) + (b2 * (L1 - P))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (- (x1 * (L1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (- (x1 * (L1 - P)))) + (b2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + (- (x1 * (L1 - P)))) + (b2 * (L1 - P))) + (- (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 + (- (x1 * (L1 - P)))) + (b2 * (L1 - P))) + (- (x * (L2 - P)))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (x1 * (L1 - P))) + (b2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((- (x1 * (L1 - P))) + (b2 * (L1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((- (x1 * (L1 - P))) + (b2 * (L1 - P)))) + (- (x * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + ((- (x1 * (L1 - P))) + (b2 * (L1 - P)))) + (- (x * (L2 - P)))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- (x * (L2 - P))) + (b3 * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((- (x1 * (L1 - P))) + (b2 * (L1 - P)))) + ((- (x * (L2 - P))) + (b3 * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b2 - x1 is V11() real ext-real Element of REAL
(b2 - x1) * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((b2 - x1) * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((b2 - x1) * (L1 - P))) + ((- (x * (L2 - P))) + (b3 * (L2 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
b3 - x is V11() real ext-real Element of REAL
(b3 - x) * (L2 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((b2 - x1) * (L1 - P))) + ((b3 - x) * (L2 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b2 - x1) * (c1 * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b2 - x1) * (c2 * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b2 - x1) * (c1 * (x2 - x1))) + ((b2 - x1) * (c2 * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (((b2 - x1) * (c1 * (x2 - x1))) + ((b2 - x1) * (c2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b3 - x) * ((d1 * (x2 - x1)) + (d2 * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (((b2 - x1) * (c1 * (x2 - x1))) + ((b2 - x1) * (c2 * (y1 - x1))))) + ((b3 - x) * ((d1 * (x2 - x1)) + (d2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b3 - x) * (d1 * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b3 - x) * (d2 * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b3 - x) * (d1 * (x2 - x1))) + ((b3 - x) * (d2 * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (((b2 - x1) * (c1 * (x2 - x1))) + ((b2 - x1) * (c2 * (y1 - x1))))) + (((b3 - x) * (d1 * (x2 - x1))) + ((b3 - x) * (d2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b2 - x1) * c1 is V11() real ext-real Element of REAL
((b2 - x1) * c1) * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c1) * (x2 - x1)) + ((b2 - x1) * (c2 * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((((b2 - x1) * c1) * (x2 - x1)) + ((b2 - x1) * (c2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + ((b2 - x1) * (c2 * (y1 - x1))))) + (((b3 - x) * (d1 * (x2 - x1))) + ((b3 - x) * (d2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b2 - x1) * c2 is V11() real ext-real Element of REAL
((b2 - x1) * c2) * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c1) * (x2 - x1)) + (((b2 - x1) * c2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b2 - x1) * c2) * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b2 - x1) * c2) * (y1 - x1)))) + (((b3 - x) * (d1 * (x2 - x1))) + ((b3 - x) * (d2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b3 - x) * d1 is V11() real ext-real Element of REAL
((b3 - x) * d1) * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b3 - x) * d1) * (x2 - x1)) + ((b3 - x) * (d2 * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b2 - x1) * c2) * (y1 - x1)))) + ((((b3 - x) * d1) * (x2 - x1)) + ((b3 - x) * (d2 * (y1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(b3 - x) * d2 is V11() real ext-real Element of REAL
((b3 - x) * d2) * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b3 - x) * d1) * (x2 - x1)) + (((b3 - x) * d2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b2 - x1) * c2) * (y1 - x1)))) + ((((b3 - x) * d1) * (x2 - x1)) + (((b3 - x) * d2) * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (((b2 - x1) * c1) * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1))) + ((((b3 - x) * d1) * (x2 - x1)) + (((b3 - x) * d2) * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1))) + (((b3 - x) * d1) * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1))) + (((b3 - x) * d1) * (x2 - x1))) + (((b3 - x) * d2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b3 - x) * d1) * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b3 - x) * d1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x1 + (((b2 - x1) * c1) * (x2 - x1))) + (((b3 - x) * d1) * (x2 - x1))) + (((b2 - x1) * c2) * (y1 - x1))) + (((b3 - x) * d2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c1) * (x2 - x1)) + (((b3 - x) * d1) * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b3 - x) * d1) * (x2 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b3 - x) * d1) * (x2 - x1)))) + (((b2 - x1) * c2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b3 - x) * d1) * (x2 - x1)))) + (((b2 - x1) * c2) * (y1 - x1))) + (((b3 - x) * d2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c2) * (y1 - x1)) + (((b3 - x) * d2) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) * (x2 - x1)) + (((b3 - x) * d1) * (x2 - x1)))) + ((((b2 - x1) * c2) * (y1 - x1)) + (((b3 - x) * d2) * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b2 - x1) * c1) + ((b3 - x) * d1) is V11() real ext-real Element of REAL
(((b2 - x1) * c1) + ((b3 - x) * d1)) * (x2 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((((b2 - x1) * c1) + ((b3 - x) * d1)) * (x2 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) + ((b3 - x) * d1)) * (x2 - x1))) + ((((b2 - x1) * c2) * (y1 - x1)) + (((b3 - x) * d2) * (y1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((b2 - x1) * c2) + ((b3 - x) * d2) is V11() real ext-real Element of REAL
(((b2 - x1) * c2) + ((b3 - x) * d2)) * (y1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((((b2 - x1) * c1) + ((b3 - x) * d1)) * (x2 - x1))) + ((((b2 - x1) * c2) + ((b3 - x) * d2)) * (y1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c1) + ((b3 - x) * d1)) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((b2 - x1) * c2) + ((b3 - x) * d2)) * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c₂₆ is V11() real ext-real Element of REAL
c₂₆ * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(c₂₆ * x1) + ((((b2 - x1) * c1) + ((b3 - x) * d1)) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((c₂₆ * x1) + ((((b2 - x1) * c1) + ((b3 - x) * d1)) * x2)) + ((((b2 - x1) * c2) + ((b3 - x) * d2)) * y1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
c₂₆ + (((b2 - x1) * c1) + ((b3 - x) * d1)) is V11() real ext-real Element of REAL
(c₂₆ + (((b2 - x1) * c1) + ((b3 - x) * d1))) + (((b2 - x1) * c2) + ((b3 - x) * d2)) is V11() real ext-real Element of REAL
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(y1)) is V16() Function-like set
(n,y1,y2,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * y2)) + (b₄ * P) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
bool (REAL n) is non empty set
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,x2,y1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * x2)) + (b₄ * y1) ) } is set
Line (x2,y1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
Line (y1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is Element of (n)
y2 is Element of bool (REAL n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,P,L1,L2) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * P) + (b₃ * L1)) + (b₄ * L2) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,y1,y2,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * y2)) + (b₄ * P) ) } is set
y1 is Element of (n)
y1 is Element of (n)
y2 is Element of bool (REAL n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,P,L1,L2) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * P) + (b₃ * L1)) + (b₄ * L2) ) } is set
y1 is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
L2 is V11() real ext-real Element of REAL
L2 * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- L2 is V11() real ext-real Element of REAL
1 + (- L2) is V11() real ext-real Element of REAL
(1 + (- L2)) + L2 is V11() real ext-real Element of REAL
(n,y1,P,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * P)) + (b₄ * L1) ) } is set
y1 + (L2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * y1) + (L2 * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- L2) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L2 * L1) + ((- L2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * y1) + ((L2 * L1) + ((- L2) * P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * y1) + ((- L2) * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * y1) + ((- L2) * P)) + (L2 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,y1,y2,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * y2)) + (b₄ * P) ) } is set
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,L2) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,L) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * L is V16() Function-like set
K145(x1,K174(L)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x2) is V16() Function-like complex-yielding set
K38(1) * x2 is V16() Function-like set
K145(L1,K174(x2)) is V16() Function-like set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x2,L1) is Element of bool (REAL n)
{ (((1 - b₁) * x2) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x1,K174(x2)) is V16() Function-like set
(n,x2,x1,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x2) + (b₃ * x1)) + (b₄ * L1) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
(n,x1,y1,y2) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * y1)) + (b₄ * y2) ) } is set
P is non empty Element of bool (REAL n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(x1,K174(y2)) is V16() Function-like set
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(y2)) is V16() Function-like set
(n,y2,x1,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y2) + (b₃ * x1)) + (b₄ * P) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y2,P) is Element of bool (REAL n)
{ (((1 - b₁) * y2) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y2) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y2 is V16() Function-like set
K145(x1,K174(y2)) is V16() Function-like set
P - y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(y2)) is V16() Function-like set
(n,y2,x1,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y2) + (b₃ * x1)) + (b₄ * P) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L1) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(x1,K174(P)) is V16() Function-like set
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L1,K174(P)) is V16() Function-like set
(n,P,x1,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * P) + (b₃ * x1)) + (b₄ * L1) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,L2) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * L1 is V16() Function-like set
K145(P,K174(L1)) is V16() Function-like set
L2 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L2,K174(L1)) is V16() Function-like set
(n,L1,P,L2) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * L1) + (b₃ * P)) + (b₄ * L2) ) } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,y1,y2,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * y1) + (b₃ * y2)) + (b₄ * P) ) } is set
L1 is Element of bool (REAL n)
Line (y1,P) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * P)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
P - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(y1)) is V16() Function-like set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is Element of (n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(L1,K174(x1)) is V16() Function-like set
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x1,K174(x1)) is V16() Function-like set
(n,x1,L1,x1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * L1)) + (b₄ * x1) ) } is set
L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
L + x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(L + x9) + x2 is V11() real ext-real Element of REAL
L * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * x1) + (x9 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * x1) + (x9 * L1)) + (x2 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((L1 - x1),(x1 - x1))| is V11() real ext-real Element of REAL
L2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L2,K174(x1)) is V16() Function-like set
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * (L1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (x9 * (L1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (x9 * (L1 - x1))) + (x2 * (x1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- x1) + ((x1 + (x9 * (L1 - x1))) + (x2 * (x1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (L1 - x1)) + (x2 * (x1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((x9 * (L1 - x1)) + (x2 * (x1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- x1) + (x1 + ((x9 * (L1 - x1)) + (x2 * (x1 - x1)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- x1) + x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- x1) + x1) + ((x9 * (L1 - x1)) + (x2 * (x1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
(0* n) + ((x9 * (L1 - x1)) + (x2 * (x1 - x1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x1 - x1),(x1 - x1))| is V11() real ext-real Element of REAL
|(((x9 * (L1 - x1)) + (x2 * (x1 - x1))),(x1 - x1))| is V11() real ext-real Element of REAL
|((x9 * (L1 - x1)),(x1 - x1))| is V11() real ext-real Element of REAL
|((x2 * (x1 - x1)),(x1 - x1))| is V11() real ext-real Element of REAL
|((x9 * (L1 - x1)),(x1 - x1))| + |((x2 * (x1 - x1)),(x1 - x1))| is V11() real ext-real Element of REAL
x9 * |((L1 - x1),(x1 - x1))| is V11() real ext-real Element of REAL
(x9 * |((L1 - x1),(x1 - x1))|) + |((x2 * (x1 - x1)),(x1 - x1))| is V11() real ext-real Element of REAL
x2 * |((x1 - x1),(x1 - x1))| is V11() real ext-real Element of REAL
0 * (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (L1 - x1)) + (0 * (x1 - x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (L1 - x1)) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,L2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
Line (x1,L1) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
L1 is Element of (n)
L2 is Element of (n)
x1 is Element of (n)
L is Element of (n)
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is Element of (n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n,x1,L2,L1) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * x1) + (b₃ * L2)) + (b₄ * L1) ) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x1,K174(x1)) is V16() Function-like set
L2 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(L2,K174(L1)) is V16() Function-like set
L is V11() real ext-real Element of REAL
L * (L2 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 + L is V11() real ext-real Element of REAL
- L is V11() real ext-real Element of REAL
(1 + L) + (- L) is V11() real ext-real Element of REAL
x1 + (L * (L2 - L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + (L * (L2 - L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- L) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * L2) + ((- L) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + ((L * L2) + ((- L) * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * x1) + (L * L2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * x1) + (L * L2)) + ((- L) * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(P) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * P is V16() Function-like set
K145(L1,K174(P)) is V16() Function-like set
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
|((L1 - P),(L1 - P))| is V11() real ext-real Element of REAL
L2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (P,L2) is Element of bool (REAL n)
{ (((1 - b₁) * P) + (b₁ * L2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x1,L1) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * L1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) * L1 is V16() Function-like set
K145(x1,K174(L1)) is V16() Function-like set
P - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(P,K174(L1)) is V16() Function-like set
|((x1 - L1),(P - L1))| is V11() real ext-real Element of REAL
(n,L1,x1,P) is non empty Element of bool (REAL n)
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : ex b₂, b₃, b₄ being V11() real ext-real Element of REAL st
( (b₂ + b₃) + b₄ = 1 & b₁ = ((b₂ * L1) + (b₃ * x1)) + (b₄ * P) ) } is set
L is V11() real ext-real Element of REAL
x9 is V11() real ext-real Element of REAL
L + x9 is V11() real ext-real Element of REAL
x2 is V11() real ext-real Element of REAL
(L + x9) + x2 is V11() real ext-real Element of REAL
L * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * L1) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((L * L1) + (x9 * x1)) + (x2 * P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 + L is V11() real ext-real Element of REAL
(x2 + L) + x9 is V11() real ext-real Element of REAL
L2 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L2,K174(P)) is V16() Function-like set
- P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x2 * P) + (L * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x2 * P) + (L * L1)) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- P) + (((x2 * P) + (L * L1)) + (x9 * x1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + (L * (L1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x1,K174(P)) is V16() Function-like set
x9 * (x1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(P + (L * (L1 - P))) + (x9 * (x1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- P) + ((P + (L * (L1 - P))) + (x9 * (x1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L * (L1 - P)) + (x9 * (x1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
P + ((L * (L1 - P)) + (x9 * (x1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- P) + (P + ((L * (L1 - P)) + (x9 * (x1 - P)))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- P) + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((- P) + P) + ((L * (L1 - P)) + (x9 * (x1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(0* n) + ((L * (L1 - P)) + (x9 * (x1 - P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x1 - L1),(L1 - P))| is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (- L1) is V16() Function-like set
((- 1) * P) + (- (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x1 - L1),(((- 1) * P) + (- (- L1))))| is V11() real ext-real Element of REAL
P + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- 1) * (P + (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|((x1 - L1),((- 1) * (P + (- L1))))| is V11() real ext-real Element of REAL
(- 1) * |((x1 - L1),(P - L1))| is V11() real ext-real Element of REAL
(0* n) + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - ((0* n) + P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((0* n) + P)) is V16() Function-like complex-yielding set
K38(1) * ((0* n) + P) is V16() Function-like set
K145(x1,K174(((0* n) + P))) is V16() Function-like set
L1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(L1,K174(L1)) is V16() Function-like set
(L1 - L1) + P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - ((L1 - L1) + P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(((L1 - L1) + P)) is V16() Function-like complex-yielding set
K38(1) * ((L1 - L1) + P) is V16() Function-like set
K145(x1,K174(((L1 - L1) + P))) is V16() Function-like set
x1 - (L1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((L1 - L1)) is V16() Function-like complex-yielding set
K38(1) * (L1 - L1) is V16() Function-like set
K145(x1,K174((L1 - L1))) is V16() Function-like set
(x1 - (L1 - L1)) - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145((x1 - (L1 - L1)),K174(P)) is V16() Function-like set
(x1 - L1) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 - L1) + L1) - P is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(((x1 - L1) + L1),K174(P)) is V16() Function-like set
(x1 - L1) + (L1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
|(((L * (L1 - P)) + (x9 * (x1 - P))),(L1 - P))| is V11() real ext-real Element of REAL
|((L * (L1 - P)),(L1 - P))| is V11() real ext-real Element of REAL
|((x9 * (x1 - P)),(L1 - P))| is V11() real ext-real Element of REAL
|((L * (L1 - P)),(L1 - P))| + |((x9 * (x1 - P)),(L1 - P))| is V11() real ext-real Element of REAL
L * |((L1 - P),(L1 - P))| is V11() real ext-real Element of REAL
(L * |((L1 - P),(L1 - P))|) + |((x9 * (x1 - P)),(L1 - P))| is V11() real ext-real Element of REAL
|((x1 - P),(L1 - P))| is V11() real ext-real Element of REAL
x9 * |((x1 - P),(L1 - P))| is V11() real ext-real Element of REAL
(L * |((L1 - P),(L1 - P))|) + (x9 * |((x1 - P),(L1 - P))|) is V11() real ext-real Element of REAL
|((x1 - L1),(L1 - P))| + |((L1 - P),(L1 - P))| is V11() real ext-real Element of REAL
x9 * (|((x1 - L1),(L1 - P))| + |((L1 - P),(L1 - P))|) is V11() real ext-real Element of REAL
(L * |((L1 - P),(L1 - P))|) + (x9 * (|((x1 - L1),(L1 - P))| + |((L1 - P),(L1 - P))|)) is V11() real ext-real Element of REAL
(L + x9) * |((L1 - P),(L1 - P))| is V11() real ext-real Element of REAL
- L is V11() real ext-real Element of REAL
L1 + (- P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 + (- P)) - (x1 - P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((x1 - P)) is V16() Function-like complex-yielding set
K38(1) * (x1 - P) is V16() Function-like set
K145((L1 + (- P)),K174((x1 - P))) is V16() Function-like set
L * ((L1 + (- P)) - (x1 - P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(L1,K174(x1)) is V16() Function-like set
(- P) - (- P) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174((- P)) is V16() Function-like complex-yielding set
K38(1) * (- P) is V16() Function-like set
K145((- P),K174((- P))) is V16() Function-like set
(L1 - x1) + ((- P) - (- P)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * ((L1 - x1) + ((- P) - (- P))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 - x1) + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * ((L1 - x1) + (0* n)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L * (L1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is Element of (n)
y2 is Element of (n)
P is Element of (n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is Element of (n)
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * L1 is V16() Function-like set
K145(L,K174(L1)) is V16() Function-like set
x1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x1,K174(L1)) is V16() Function-like set
x9 is V11() real ext-real Element of REAL
x9 * (x1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (L1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
Line (L,x2) is Element of bool (REAL n)
{ (((1 - b₁) * L) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
1 - x9 is V11() real ext-real Element of REAL
(1 - x9) * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - x9) * L1) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(L) is V16() Function-like complex-yielding set
K38(1) * L is V16() Function-like set
K145(x2,K174(L)) is V16() Function-like set
x1 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) * x1 is V16() Function-like set
K145(x1,K174(x1)) is V16() Function-like set
b is V11() real ext-real Element of REAL
b * (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 / b is V11() real ext-real Element of REAL
(1 / b) * b is V11() real ext-real Element of REAL
((1 / b) * b) * (x1 - x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 / b) * (x2 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- (x9 * L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * (x9 * L1) is V16() Function-like set
(1 * L1) + (- (x9 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * L1) + (- (x9 * L1))) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L1 + (- (x9 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L1 + (- (x9 * L1))) + (x9 * x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * x1) + (- (x9 * L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * x1) + (- (x9 * L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 - L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K145(x1,K174(L1)) is V16() Function-like set
x9 * (x1 - L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (x1 - L1)) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set
x1 + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (0* n)) + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * ((x1 + (0* n)) + (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * ((x1 + (0* n)) + (- L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- x1) + x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + ((- x1) + x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + ((- x1) + x1)) + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * ((x1 + ((- x1) + x1)) + (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * ((x1 + ((- x1) + x1)) + (- L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (- x1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 + (- x1)) + x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x1 + (- x1)) + x1) + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * (((x1 + (- x1)) + x1) + (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * (((x1 + (- x1)) + x1) + (- L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x1 + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x1 - x1) + (x1 + (- L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * ((x1 - x1) + (x1 + (- L1))) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * ((x1 - x1) + (x1 + (- L1)))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * ((1 / b) * (x2 - L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 * ((1 / b) * (x2 - L))) + (x9 * (x1 - L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * ((1 / b) * (x2 - L))) + (x9 * (x1 - L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 * (1 / b) is V11() real ext-real Element of REAL
(x9 * (1 / b)) * (x2 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 * (1 / b)) * (x2 - L)) + (x9 * (x1 - L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x9 * (1 / b)) * (x2 - L)) + (x9 * (x1 - L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x9 / b is V11() real ext-real Element of REAL
(x9 / b) * (x2 - L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 / b) * (x2 - L)) + (x9 * (x1 - L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x9 / b) * (x2 - L)) + (x9 * (x1 - L1))) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L + (- L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L + (- L1)) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 / b) * (x2 - L)) + ((L + (- L1)) + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(- L1) + L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L + ((- L1) + L1) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 / b) * (x2 - L)) + (L + ((- L1) + L1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L + (0* n) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 / b) * (x2 - L)) + (L + (0* n)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((x9 / b) * (x2 - L)) + L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 / b) * x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(x9 / b) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
- ((x9 / b) * L) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K38(1) * ((x9 / b) * L) is V16() Function-like set
((x9 / b) * x2) + (- ((x9 / b) * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(((x9 / b) * x2) + (- ((x9 / b) * L))) + L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L + (- ((x9 / b) * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(L + (- ((x9 / b) * L))) + ((x9 / b) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(1 * L) + (- ((x9 / b) * L)) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 * L) + (- ((x9 / b) * L))) + ((x9 / b) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
1 - (x9 / b) is V11() real ext-real Element of REAL
(1 - (x9 / b)) * L is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
((1 - (x9 / b)) * L) + ((x9 / b) * x2) is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
x1 is Element of (n)
x2 is Element of (n)
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
(n) is non empty Element of bool (bool (REAL n))
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
y2 is Element of (n)
P is Element of (n)
L1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
L2 is Element of (n)
Line (L1,y1) is Element of bool (REAL n)
{ (((1 - b₁) * L1) + (b₁ * y1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (y1,x1) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
L is Element of (n)
x9 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
Line (x9,x1) is Element of bool (REAL n)
{ (((1 - b₁) * x9) + (b₁ * x1)) where b₁ is V11() real ext-real Element of REAL : verum } is set
n is natural V11() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V16() V19( NAT ) V20( REAL ) Function-like FinSequence-like Element of REAL * : len b₁ = n } is set
bool (REAL n) is non empty set
(n) is non empty Element of bool (bool (REAL n))
bool (bool (REAL n)) is non empty set
{ b₁ where b₁ is Element of bool (REAL n) : ex b₂, b₃, b₄ being V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n st b₁ = (n,b₂,b₃,b₄) } is set
x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
x2 - x1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(x1) is V16() Function-like complex-yielding set
K38(1) is V11() real ext-real non positive set
K38(1) * x1 is V16() Function-like set
K145(x2,K174(x1)) is V16() Function-like set
Line (x1,x2) is Element of bool (REAL n)
{ (((1 - b₁) * x1) + (b₁ * x2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
y2 - y1 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
K174(y1) is V16() Function-like complex-yielding set
K38(1) * y1 is V16() Function-like set
K145(y2,K174(y1)) is V16() Function-like set
Line (y1,y2) is Element of bool (REAL n)
{ (((1 - b₁) * y1) + (b₁ * y2)) where b₁ is V11() real ext-real Element of REAL : verum } is set
P is Element of (n)
(n) is non empty Element of bool (bool (REAL n))
{ (Line (b₁,b₂)) where b₁, b₂ is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n : verum } is set
L1 is Element of (n)
L2 is Element of (n)
0* n is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() V69(n) FinSequence-like Element of REAL n
n |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-yielding V34() V35() FinSequence-like Element of n -tuples_on REAL
Seg n is V45() V46() V47() V48() V49() V50() Element of bool NAT
K277((Seg n),0) is V16() V19( Seg n) V20( RAT ) V20( INT ) V20({0}) Function-like V30( Seg n,{0}) complex-yielding V34() V35() V36() Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is V20( RAT ) V20( INT ) complex-yielding V34() V35() V36() set
bool [:(Seg n),{0}:] is non empty set