REAL is non empty non trivial non finite V72() V73() V74() V78() V295() V296() V298() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V72() V73() V74() V75() V76() V77() V78() V293() V295() Element of bool REAL
bool REAL is non empty non trivial non finite cup-closed diff-closed preBoolean set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V72() V73() V74() V75() V76() V77() V78() V293() V295() set
bool omega is non empty non trivial non finite cup-closed diff-closed preBoolean set
bool NAT is non empty non trivial non finite cup-closed diff-closed preBoolean set
COMPLEX is non empty non trivial non finite V72() V78() set
RAT is non empty non trivial non finite V72() V73() V74() V75() V78() set
INT is non empty non trivial non finite V72() V73() V74() V75() V76() V78() set
[:REAL,REAL:] is non empty non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
bool [:REAL,REAL:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
{} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
{{},1} is non empty finite V34() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
K392() is set
bool K392() is non empty cup-closed diff-closed preBoolean set
K393() is Element of bool K392()
K458() is set
{{}} is non empty trivial functional finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
{{}} * is non empty functional FinSequence-membered FinSequenceSet of {{}}
[:({{}} *),{{}}:] is non empty Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:({{}} *),{{}}:] is non empty cup-closed diff-closed preBoolean set
PFuncs (({{}} *),{{}}) is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:COMPLEX,COMPLEX:] is non empty non trivial Relation-like non finite complex-valued set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial Relation-like non finite complex-valued set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:[:REAL,REAL:],REAL:] is non empty non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:RAT,RAT:] is non empty non trivial Relation-like RAT -valued non finite complex-valued ext-real-valued real-valued set
bool [:RAT,RAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:[:RAT,RAT:],RAT:] is non empty non trivial Relation-like RAT -valued non finite complex-valued ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:INT,INT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued set
bool [:INT,INT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:[:INT,INT:],INT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:[:NAT,NAT:],NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
[:COMPLEX,REAL:] is non empty non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
bool [:COMPLEX,REAL:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
K516() is Relation-like NAT -defined Function-like total set
3 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
dom {} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() set
rng {} is empty trivial Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative V50() complex-valued ext-real-valued real-valued natural-valued V66() decreasing non-decreasing non-increasing V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() set
NATOrd is Relation-like NAT -defined NAT -valued complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
{ [b1,b2] where b1, b2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : b1 <= b2 } is set
OrderedNAT is non empty transitive antisymmetric connected well_founded quasi_ordered Dickson RelStr
RelStr(# NAT,NATOrd #) is non empty strict RelStr
<*> REAL is empty proper Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() FinSequence of REAL
[:NAT,REAL:] is non empty non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
Sum (<*> REAL) is V42() V43() ext-real Element of REAL
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() V44() ext-real non positive non negative V49() complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() Element of NAT
card {} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() set
CR is set
R is set
IR is set
{CR} is non empty trivial finite 1 -element set
R \ {CR} is Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
IR \ {CR} is Element of bool IR
bool IR is non empty cup-closed diff-closed preBoolean set
R \/ {CR} is non empty set
(IR \ {CR}) \/ {CR} is non empty set
IR \/ {CR} is non empty set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Seg R is finite R -element V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
IR - 1 is V42() V43() ext-real Element of REAL
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : ( 1 <= b1 & b1 <= R ) } is set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R - 1 is V42() V43() ext-real Element of REAL
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
- 1 is V42() V43() ext-real non positive Element of REAL
IR + (- 1) is V42() V43() ext-real Element of REAL
R + (- 1) is V42() V43() ext-real Element of REAL
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(IR - 1) + 1 is V42() V43() ext-real Element of REAL
(R - 1) + 1 is V42() V43() ext-real Element of REAL
R is Relation-like Function-like finite-support set
IR is set
R | IR is Relation-like Function-like set
support (R | IR) is set
support R is finite set
CR is set
(R | IR) . CR is set
dom (R | IR) is set
R . CR is set
R is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
len R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(len R) |-> 0 is Relation-like NAT -defined NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding FinSequence-yielding finite-support Element of (len R) -tuples_on NAT
(len R) -tuples_on NAT is FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b1 = len R } is set
Seg (len R) is finite len R -element V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
(Seg (len R)) --> 0 is Relation-like Seg (len R) -defined RAT -valued INT -valued {0} -valued Function-like total V18( Seg (len R),{0}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(Seg (len R)),{0}:]
{0} is non empty trivial functional finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
[:(Seg (len R)),{0}:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg (len R)),{0}:] is non empty finite V34() cup-closed diff-closed preBoolean set
dom R is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom ((len R) |-> 0) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R . IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R . CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
((len R) |-> 0) . IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal FinSequence-like V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR -' IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is Relation-like R -defined Function-like total finite-support set
FCR is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not CR -' IR <= b1 } is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR + A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (IR + A) is set
zz is set
zz is set
FCR is set
FCR is Relation-like Function-like set
dom FCR is set
A is Relation-like CR -' IR -defined Function-like total finite-support set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is set
IR + zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (IR + zz) is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR + zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (IR + zz) is set
FCR is Relation-like CR -' IR -defined Function-like total finite-support set
A is Relation-like CR -' IR -defined Function-like total finite-support set
dom FCR is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool (CR -' IR)
bool (CR -' IR) is non empty finite V34() cup-closed diff-closed preBoolean set
dom A is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool (CR -' IR)
zz is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not CR -' IR <= b1 } is set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR + zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (IR + zz) is set
A . zz is set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,IR,CR,FIR) is Relation-like CR -' IR -defined Function-like total finite-support set
CR -' IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR is set
rng (R,IR,CR,FIR) is set
dom (R,IR,CR,FIR) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool (CR -' IR)
bool (CR -' IR) is non empty finite V34() cup-closed diff-closed preBoolean set
A is set
(R,IR,CR,FIR) . A is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not CR -' IR <= b1 } is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR + zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (IR + zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is Relation-like R -defined Function-like total finite-support set
(R,IR,CR,FIR) is Relation-like CR -' IR -defined Function-like total finite-support set
CR -' IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
CR is Relation-like R -defined Function-like total finite-support set
FIR is Relation-like R -defined Function-like total finite-support set
(R,0,(IR + 1),CR) is Relation-like (IR + 1) -' 0 -defined Function-like total finite-support set
(IR + 1) -' 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R,0,(IR + 1),FIR) is Relation-like (IR + 1) -' 0 -defined Function-like total finite-support set
(R,(IR + 1),R,CR) is Relation-like R -' (IR + 1) -defined Function-like total finite-support set
R -' (IR + 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R,(IR + 1),R,FIR) is Relation-like R -' (IR + 1) -defined Function-like total finite-support set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
((IR + 1) + 0) -' 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R,0,(IR + 1),FIR) . Z is set
0 + Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (0 + Z) is set
CR . Z is set
FIR . Z is set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z -' (IR + 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR + 1) - (IR + 1) is V42() V43() ext-real Element of REAL
Z - (IR + 1) is V42() V43() ext-real Element of REAL
R - (IR + 1) is V42() V43() ext-real Element of REAL
(R,(IR + 1),R,FIR) . (Z -' (IR + 1)) is set
(IR + 1) + (Z -' (IR + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FIR . ((IR + 1) + (Z -' (IR + 1))) is set
CR . Z is set
FIR . Z is set
Z is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not R <= b1 } is set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . Z is set
FIR . Z is set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . Z is set
FIR . Z is set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is non empty set
bool R is non empty cup-closed diff-closed preBoolean set
IR is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
{ b1 where b1 is Element of bool R : ( b1 is finite & not b1 is empty & card b1 c= IR ) } is set
R is non empty set
IR is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(R,IR) is set
bool R is non empty cup-closed diff-closed preBoolean set
{ b1 where b1 is Element of bool R : ( b1 is finite & not b1 is empty & card b1 c= IR ) } is set
the Element of R is Element of R
IR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
{ the Element of R} is non empty trivial finite 1 -element Element of bool R
card { the Element of R} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of omega
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not 1 <= b1 } is set
{ the Element of R} is non empty trivial finite 1 -element Element of bool R
card { the Element of R} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of omega
FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
{ the Element of R} is non empty trivial finite 1 -element Element of bool R
card { the Element of R} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of omega
{ the Element of R} is non empty trivial finite 1 -element Element of bool R
card { the Element of R} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of omega
R is non empty transitive antisymmetric RelStr
the carrier of R is non empty set
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is finite Element of bool the carrier of R
FCR is set
A is set
{FCR} is non empty trivial finite 1 -element set
A \/ {FCR} is non empty set
zz is Element of the carrier of R
zz is Element of the carrier of R
{zz} is non empty trivial finite 1 -element Element of bool the carrier of R
A \/ {zz} is non empty set
Z is set
[zz,Z] is V1() set
{zz,Z} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
zz is Element of the carrier of R
zz is Element of the carrier of R
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
zz is Element of the carrier of R
Z is Element of the carrier of R
aStart is set
[FCR,aStart] is V1() set
{FCR,aStart} is non empty finite set
{{FCR,aStart},{FCR}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty finite set
{{zz,aStart},{zz}} is non empty finite V34() set
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
Z is Element of the carrier of R
aStart is set
[Z,aStart] is V1() set
{Z,aStart} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
aStart is set
[Z,aStart] is V1() set
{Z,aStart} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
Z is Element of the carrier of R
aStart is set
[Z,aStart] is V1() set
{Z,aStart} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
aStart is set
[Z,aStart] is V1() set
{Z,aStart} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
Z is Element of the carrier of R
FCR is set
A is set
zz is Element of the carrier of R
{FCR} is non empty trivial finite 1 -element set
A \/ {FCR} is non empty set
R is non empty transitive antisymmetric RelStr
the carrier of R is non empty set
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is finite Element of bool the carrier of R
FCR is set
A is set
{FCR} is non empty trivial finite 1 -element set
A \/ {FCR} is non empty set
zz is Element of the carrier of R
zz is Element of the carrier of R
{zz} is non empty trivial finite 1 -element Element of bool the carrier of R
A \/ {zz} is non empty set
Z is set
[Z,zz] is V1() set
{Z,zz} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,zz},{Z}} is non empty finite V34() set
zz is Element of the carrier of R
zz is Element of the carrier of R
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
zz is Element of the carrier of R
Z is Element of the carrier of R
aStart is set
[aStart,FCR] is V1() set
{aStart,FCR} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,FCR},{aStart}} is non empty finite V34() set
aStart is set
[aStart,FCR] is V1() set
{aStart,FCR} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,FCR},{aStart}} is non empty finite V34() set
[aStart,zz] is V1() set
{aStart,zz} is non empty finite set
{{aStart,zz},{aStart}} is non empty finite V34() set
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
Z is Element of the carrier of R
aStart is set
[aStart,Z] is V1() set
{aStart,Z} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,Z},{aStart}} is non empty finite V34() set
aStart is set
[aStart,Z] is V1() set
{aStart,Z} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,Z},{aStart}} is non empty finite V34() set
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
Z is Element of the carrier of R
aStart is set
[aStart,Z] is V1() set
{aStart,Z} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,Z},{aStart}} is non empty finite V34() set
aStart is set
[aStart,Z] is V1() set
{aStart,Z} is non empty finite set
{aStart} is non empty trivial finite 1 -element set
{{aStart,Z},{aStart}} is non empty finite V34() set
[FCR,zz] is V1() set
{FCR,zz} is non empty finite set
{{FCR,zz},{FCR}} is non empty finite V34() set
[zz,FCR] is V1() set
{zz,FCR} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,FCR},{zz}} is non empty finite V34() set
Z is Element of the carrier of R
FCR is set
A is set
zz is Element of the carrier of R
{FCR} is non empty trivial finite 1 -element set
A \/ {FCR} is non empty set
R is non empty transitive antisymmetric RelStr
the carrier of R is non empty set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
IR . 0 is Element of the carrier of R
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
[(IR . 0),(IR . FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . 0),(IR . FCR)} is non empty finite set
{(IR . 0)} is non empty trivial finite 1 -element set
{{(IR . 0),(IR . FCR)},{(IR . 0)}} is non empty finite V34() set
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
FCR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . A is Element of the carrier of R
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . A is Element of the carrier of R
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . A is Element of the carrier of R
[(IR . FCR),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . FCR),(IR . A)} is non empty finite set
{(IR . FCR)} is non empty trivial finite 1 -element set
{{(IR . FCR),(IR . A)},{(IR . FCR)}} is non empty finite V34() set
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . FCR)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . FCR)},{(IR . (FCR + 1))}} is non empty finite V34() set
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . A is Element of the carrier of R
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . A is Element of the carrier of R
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
FCR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . A is Element of the carrier of R
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
R is non empty RelStr
the carrier of R is non empty set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
R is non empty transitive RelStr
the carrier of R is non empty set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
IR . 0 is Element of the carrier of R
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
[(IR . 0),(IR . FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . 0),(IR . FCR)} is non empty finite set
{(IR . 0)} is non empty trivial finite 1 -element set
{{(IR . 0),(IR . FCR)},{(IR . 0)}} is non empty finite V34() set
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
FCR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . (FCR + 1) is Element of the carrier of R
IR . A is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . (FCR + 1) is Element of the carrier of R
IR . A is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . A is Element of the carrier of R
[(IR . FCR),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . FCR),(IR . A)} is non empty finite set
{(IR . FCR)} is non empty trivial finite 1 -element set
{{(IR . FCR),(IR . A)},{(IR . FCR)}} is non empty finite V34() set
IR . (FCR + 1) is Element of the carrier of R
[(IR . (FCR + 1)),(IR . FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . FCR)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . FCR)},{(IR . (FCR + 1))}} is non empty finite V34() set
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . (FCR + 1) is Element of the carrier of R
IR . A is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
IR . (FCR + 1) is Element of the carrier of R
IR . A is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . FCR is Element of the carrier of R
FCR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . (FCR + 1) is Element of the carrier of R
IR . A is Element of the carrier of R
[(IR . (FCR + 1)),(IR . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . (FCR + 1)),(IR . A)} is non empty finite set
{(IR . (FCR + 1))} is non empty trivial finite 1 -element set
{{(IR . (FCR + 1)),(IR . A)},{(IR . (FCR + 1))}} is non empty finite V34() set
R is non empty transitive RelStr
the carrier of R is non empty set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
IR is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
dom IR is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
rng IR is non empty set
FCR is set
the InternalRel of R -Seg FCR is set
( the InternalRel of R -Seg FCR) /\ (rng IR) is set
A is set
IR . A is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . zz is Element of the carrier of R
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR . zz is Element of the carrier of R
[(IR . zz),(IR . zz)] is V1() Element of [: the carrier of R, the carrier of R:]
{(IR . zz),(IR . zz)} is non empty finite set
{(IR . zz)} is non empty trivial finite 1 -element set
{{(IR . zz),(IR . zz)},{(IR . zz)}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . Z is Element of the carrier of R
R is set
bool R is non empty cup-closed diff-closed preBoolean set
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
IR is Element of R
{IR} is non empty trivial finite 1 -element set
<*IR*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
CR is finite Element of bool R
FIR is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric transitive Element of bool [:R,R:]
SgmX (FIR,CR) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
len (SgmX (FIR,CR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
card CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
rng (SgmX (FIR,CR)) is finite set
R is epsilon-transitive epsilon-connected ordinal set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support IR is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
SgmX ((RelIncl R),(support IR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),(support IR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
dom IR is Element of bool R
rng IR is V72() V73() V74() V75() V76() V77() V295() Element of bool REAL
[:R,NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:R,NAT:] is non empty cup-closed diff-closed preBoolean set
FIR is Relation-like R -defined NAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
FCR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
A is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal set
bool R is non empty cup-closed diff-closed preBoolean set
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support IR is finite Element of bool R
SgmX ((RelIncl R),(support IR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),(support IR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
CR is finite Element of bool R
(support IR) \/ CR is finite Element of bool R
SgmX ((RelIncl R),((support IR) \/ CR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),((support IR) \/ CR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
FIR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
FCR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Sum FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
((support IR) \/ CR) \ (support IR) is finite Element of bool R
SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR))) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
(SgmX ((RelIncl R),(support IR))) ^ (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR)))) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * ((SgmX ((RelIncl R),(support IR))) ^ (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR))))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
dom IR is Element of bool R
field (RelIncl R) is set
rng (SgmX ((RelIncl R),((support IR) \/ CR))) is finite set
rng (SgmX ((RelIncl R),(support IR))) is finite set
rng (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR)))) is finite set
rng ((SgmX ((RelIncl R),(support IR))) ^ (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR))))) is finite set
(support IR) \/ (((support IR) \/ CR) \ (support IR)) is finite Element of bool R
S0max is non empty epsilon-transitive epsilon-connected ordinal set
rng IR is V72() V73() V74() V75() V76() V77() V295() Element of bool REAL
[:S0max,REAL:] is non empty non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
bool [:S0max,REAL:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
S02 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng S02 is finite set
b0t is non empty Relation-like S0max -defined REAL -valued Function-like total V18(S0max, REAL ) complex-valued ext-real-valued real-valued Element of bool [:S0max,REAL:]
rng b0t is non empty V72() V73() V74() Element of bool REAL
(support IR) \/ (support IR) is finite Element of bool R
((support IR) \/ (support IR)) \/ CR is finite Element of bool R
(support IR) \/ ((support IR) \/ CR) is finite Element of bool R
len ((SgmX ((RelIncl R),(support IR))) ^ (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR))))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a0 is Relation-like NAT -defined S0max -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of S0max
len a0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
i0 is Relation-like NAT -defined S0max -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of S0max
len i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(len a0) + (len i0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
card (support IR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
(card (support IR)) + (len i0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
card (((support IR) \/ CR) \ (support IR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
(card (support IR)) + (card (((support IR) \/ CR) \ (support IR))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
card ((support IR) \/ CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
len (SgmX ((RelIncl R),((support IR) \/ CR))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (SgmX ((RelIncl R),((support IR) \/ CR))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom ((SgmX ((RelIncl R),(support IR))) ^ (SgmX ((RelIncl R),(((support IR) \/ CR) \ (support IR))))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
rng a0 is finite set
rng i0 is finite set
S is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
b0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
dom i0 is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
b0t * i0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
dom (b0t * i0) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
Seg (len i0) is finite len i0 -element V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
(len i0) |-> 0 is Relation-like NAT -defined NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding FinSequence-yielding finite-support Element of (len i0) -tuples_on NAT
(len i0) -tuples_on NAT is FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b1 = len i0 } is set
(Seg (len i0)) --> 0 is Relation-like Seg (len i0) -defined RAT -valued INT -valued {0} -valued Function-like total V18( Seg (len i0),{0}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(Seg (len i0)),{0}:]
{0} is non empty trivial functional finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
[:(Seg (len i0)),{0}:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg (len i0)),{0}:] is non empty finite V34() cup-closed diff-closed preBoolean set
dom ((len i0) |-> 0) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
a is set
i0 . a is set
b0t . (i0 . a) is V42() V43() ext-real Element of REAL
(b0t * i0) . a is V42() V43() ext-real Element of REAL
((len i0) |-> 0) . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal FinSequence-like V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(len i0) |-> 0 is Relation-like NAT -defined REAL -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence-yielding finite-support Element of (len i0) -tuples_on REAL
(len i0) -tuples_on REAL is FinSequenceSet of REAL
REAL * is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of REAL * : len b1 = len i0 } is set
b0t * a0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
(b0t * a0) ^ (b0t * i0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
Sum b0 is V42() V43() ext-real Element of REAL
Sum (b0t * a0) is V42() V43() ext-real Element of REAL
Sum (b0t * i0) is V42() V43() ext-real Element of REAL
(Sum (b0t * a0)) + (Sum (b0t * i0)) is V42() V43() ext-real Element of REAL
(Sum FIR) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(IR + CR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,IR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,IR) + (R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
field (RelIncl R) is set
support (IR + CR) is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
SgmX ((RelIncl R),(support (IR + CR))) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
(IR + CR) * (SgmX ((RelIncl R),(support (IR + CR)))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
FIR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
support IR is finite Element of bool R
SgmX ((RelIncl R),(support IR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),(support IR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
FCR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
support CR is finite Element of bool R
SgmX ((RelIncl R),(support CR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
CR * (SgmX ((RelIncl R),(support CR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
A is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(support IR) \/ (support CR) is finite Element of bool R
Z is finite Element of bool R
SgmX ((RelIncl R),Z) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),Z)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
CR * (SgmX ((RelIncl R),Z)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
rng (SgmX ((RelIncl R),Z)) is finite set
dom IR is Element of bool R
dom CR is Element of bool R
S01 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng S01 is finite set
rng IR is V72() V73() V74() V75() V76() V77() V295() Element of bool REAL
S02 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng S02 is finite set
rng CR is V72() V73() V74() V75() V76() V77() V295() Element of bool REAL
S0max is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
a0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
len FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (IR + CR) is Element of bool R
Seg (len FIR) is finite len FIR -element V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom FIR is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom (SgmX ((RelIncl R),Z)) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom S0max is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
dom a0 is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
i0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0t is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
len S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
len a0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S0max + a0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
len (S0max + a0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (S0max + a0) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
zz is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued finite-support FinSequence of REAL
dom zz is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max . a is V42() V43() ext-real Element of REAL
a0 . a is V42() V43() ext-real Element of REAL
zz . a is V42() V43() ext-real Element of REAL
(SgmX ((RelIncl R),(support (IR + CR)))) . a is set
(IR + CR) . ((SgmX ((RelIncl R),(support (IR + CR)))) . a) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . ((SgmX ((RelIncl R),(support (IR + CR)))) . a) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . ((SgmX ((RelIncl R),(support (IR + CR)))) . a) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR . ((SgmX ((RelIncl R),(support (IR + CR)))) . a)) + (CR . ((SgmX ((RelIncl R),(support (IR + CR)))) . a)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S is Relation-like Seg (len FIR) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(S . a) + (CR . ((SgmX ((RelIncl R),(support (IR + CR)))) . a)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n is V42() V43() ext-real Element of REAL
b is V42() V43() ext-real Element of REAL
n + b is V42() V43() ext-real Element of REAL
(S0max + a0) . a is V42() V43() ext-real Element of REAL
R is epsilon-transitive epsilon-connected ordinal set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR -' CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(IR -' CR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,IR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,IR) - (R,CR) is V42() V43() ext-real set
(IR -' CR) + CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,((IR -' CR) + CR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,(IR -' CR)) + (R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R is epsilon-transitive epsilon-connected ordinal set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
Bags R is non empty set
Bags R is non empty functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,IR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
field (RelIncl R) is set
support IR is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
dom IR is Element of bool R
SgmX ((RelIncl R),(support IR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
IR * (SgmX ((RelIncl R),(support IR))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
CR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
len CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(len CR) |-> 0 is Relation-like NAT -defined NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding FinSequence-yielding finite-support Element of (len CR) -tuples_on NAT
(len CR) -tuples_on NAT is FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b1 = len CR } is set
Seg (len CR) is finite len CR -element V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
(Seg (len CR)) --> 0 is Relation-like Seg (len CR) -defined RAT -valued INT -valued {0} -valued Function-like total V18( Seg (len CR),{0}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(Seg (len CR)),{0}:]
{0} is non empty trivial functional finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
[:(Seg (len CR)),{0}:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg (len CR)),{0}:] is non empty finite V34() cup-closed diff-closed preBoolean set
FIR is set
IR . FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
rng (SgmX ((RelIncl R),(support IR))) is finite set
dom (SgmX ((RelIncl R),(support IR))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
FCR is set
(SgmX ((RelIncl R),(support IR))) . FCR is set
dom CR is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
CR . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R --> 0 is Relation-like R -defined NAT -valued RAT -valued INT -valued Function-like total V18(R, NAT ) T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
[:R,NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:R,NAT:] is non empty cup-closed diff-closed preBoolean set
CR is set
IR . CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (IR * (SgmX ((RelIncl R),(support IR)))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
CR is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
EmptyBag CR is Relation-like CR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags CR
Bags CR is non empty set
Bags CR is non empty functional Element of bool (Bags CR)
bool (Bags CR) is non empty cup-closed diff-closed preBoolean set
(CR,R,IR,(EmptyBag CR)) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR -' R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
EmptyBag (IR -' R) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (IR -' R)
Bags (IR -' R) is non empty set
Bags (IR -' R) is non empty functional Element of bool (Bags (IR -' R))
bool (Bags (IR -' R)) is non empty cup-closed diff-closed preBoolean set
dom (CR,R,IR,(EmptyBag CR)) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool (IR -' R)
bool (IR -' R) is non empty finite V34() cup-closed diff-closed preBoolean set
FCR is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not IR -' R <= b1 } is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR,R,IR,(EmptyBag CR)) . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R + A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag CR) . (R + A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag (IR -' R)) . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR is set
(CR,R,IR,(EmptyBag CR)) . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag (IR -' R)) . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR is set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR -' R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is Relation-like CR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FCR is Relation-like CR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR + FCR is Relation-like CR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR,R,IR,(FIR + FCR)) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR,R,IR,FIR) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR,R,IR,FCR) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR,R,IR,FIR) + (CR,R,IR,FCR) is Relation-like IR -' R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not IR -' R <= b1 } is set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR,R,IR,(FIR + FCR)) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R + aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(FIR + FCR) . (R + aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . (R + aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . (R + aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(FIR . (R + aStart)) + (FCR . (R + aStart)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR,R,IR,FIR) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR,R,IR,FCR) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
((CR,R,IR,FIR) + (CR,R,IR,FCR)) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
Bags R is non empty set
Bags R is non empty functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
support (EmptyBag R) is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
IR is set
(EmptyBag R) . IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
Bags R is non empty set
Bags R is non empty functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support IR is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
dom IR is Element of bool R
dom (EmptyBag R) is Element of bool R
CR is set
IR . CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag R) . CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal set
IR is epsilon-transitive epsilon-connected ordinal set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR | IR is Relation-like IR -defined R -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued finite-support set
dom CR is Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
dom (CR | IR) is Element of bool IR
bool IR is non empty cup-closed diff-closed preBoolean set
R is epsilon-transitive epsilon-connected ordinal set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support CR is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
support IR is finite Element of bool R
FIR is set
CR . FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
R is epsilon-transitive epsilon-connected ordinal set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
IR is set
CR is set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[IR,CR] is V1() set
{IR,CR} is non empty finite set
{IR} is non empty trivial finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
[CR,IR] is V1() set
{CR,IR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,IR},{CR}} is non empty finite V34() set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),IR] is V1() set
{(EmptyBag R),IR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),IR},{(EmptyBag R)}} is non empty finite V34() set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),IR] is V1() set
{(EmptyBag R),IR} is non empty functional finite set
{{(EmptyBag R),IR},{(EmptyBag R)}} is non empty finite V34() set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[IR,CR] is V1() set
{IR,CR} is non empty functional finite set
{IR} is non empty trivial functional finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
FCR is epsilon-transitive epsilon-connected ordinal set
CR . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . FCR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is epsilon-transitive epsilon-connected ordinal set
(IR + FIR) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR . A) + (FIR . A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR + FIR) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR . A) + (FIR . A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
(IR + FIR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR . zz) + (FIR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR + FIR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR . zz) + (FIR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal set
(CR + FIR) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(IR + FIR) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR + FIR),(CR + FIR)] is V1() set
{(IR + FIR),(CR + FIR)} is non empty functional finite set
{(IR + FIR)} is non empty trivial functional finite 1 -element set
{{(IR + FIR),(CR + FIR)},{(IR + FIR)}} is non empty finite V34() set
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[IR,CR] is V1() set
{IR,CR} is non empty functional finite set
{IR} is non empty trivial functional finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR + FIR),(CR + FIR)] is V1() set
{(IR + FIR),(CR + FIR)} is non empty functional finite set
{(IR + FIR)} is non empty trivial functional finite 1 -element set
{{(IR + FIR),(CR + FIR)},{(IR + FIR)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order Element of bool [:(Bags R),(Bags R):]
R is epsilon-transitive epsilon-connected ordinal set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
R is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order (R) Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
RelStr(# (Bags R),(BagOrder R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the InternalRel of RelStr(# (Bags R),(BagOrder R) #) is Relation-like the carrier of RelStr(# (Bags R),(BagOrder R) #) -defined the carrier of RelStr(# (Bags R),(BagOrder R) #) -valued total V18( the carrier of RelStr(# (Bags R),(BagOrder R) #), the carrier of RelStr(# (Bags R),(BagOrder R) #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags R),(BagOrder R) #), the carrier of RelStr(# (Bags R),(BagOrder R) #):]
the carrier of RelStr(# (Bags R),(BagOrder R) #) is non empty set
[: the carrier of RelStr(# (Bags R),(BagOrder R) #), the carrier of RelStr(# (Bags R),(BagOrder R) #):] is non empty Relation-like set
bool [: the carrier of RelStr(# (Bags R),(BagOrder R) #), the carrier of RelStr(# (Bags R),(BagOrder R) #):] is non empty cup-closed diff-closed preBoolean set
field the InternalRel of RelStr(# (Bags R),(BagOrder R) #) is set
R --> 0 is non empty Relation-like R -defined NAT -valued RAT -valued INT -valued Function-like total V18(R, NAT ) T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
[:R,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:R,NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) +* (A,1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
dom (R --> 0) is non empty epsilon-transitive epsilon-connected ordinal Element of bool R
bool R is non empty non trivial non finite cup-closed diff-closed preBoolean set
Z is set
{A} is non empty trivial finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of bool NAT
zz is Relation-like R -defined Function-like total set
zz . Z is set
(R --> 0) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
support zz is set
Z is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
aStart is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
[:NAT, the carrier of RelStr(# (Bags R),(BagOrder R) #):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of RelStr(# (Bags R),(BagOrder R) #):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
A is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags R),(BagOrder R) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags R),(BagOrder R) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags R),(BagOrder R) #):]
zz is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags R),(BagOrder R) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags R),(BagOrder R) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags R),(BagOrder R) #):]
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
zz . (zz + 1) is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
zz . zz is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
[(zz . (zz + 1)),(zz . zz)] is V1() set
{(zz . (zz + 1)),(zz . zz)} is non empty finite set
{(zz . (zz + 1))} is non empty trivial finite 1 -element set
{{(zz . (zz + 1)),(zz . zz)},{(zz . (zz + 1))}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
zz . (Z + 1) is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
zz . Z is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
(R --> 0) +* ((zz + 1),1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
(R --> 0) +* (zz,1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S01 . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 is epsilon-transitive epsilon-connected ordinal set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not Z + 1 <= b1 } is set
SS . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . (zz + 1) is Element of the carrier of RelStr(# (Bags R),(BagOrder R) #)
[(zz . (zz + 1)),(zz . zz)] is V1() Element of [: the carrier of RelStr(# (Bags R),(BagOrder R) #), the carrier of RelStr(# (Bags R),(BagOrder R) #):]
{(zz . (zz + 1)),(zz . zz)} is non empty finite set
{(zz . (zz + 1))} is non empty trivial finite 1 -element set
{{(zz . (zz + 1)),(zz . zz)},{(zz . (zz + 1))}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like Bags R -defined Bags R -valued Element of bool [:(Bags R),(Bags R):]
CR is set
[CR,CR] is V1() set
{CR,CR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,CR},{CR}} is non empty finite V34() set
CR is set
FIR is set
[CR,FIR] is V1() set
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() set
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
Z is epsilon-transitive epsilon-connected ordinal set
zz . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is set
FIR is set
FCR is set
[CR,FIR] is V1() set
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
[CR,FCR] is V1() set
{CR,FCR} is non empty finite set
{{CR,FCR},{CR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is epsilon-transitive epsilon-connected ordinal set
zz . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
zz . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
SS is epsilon-transitive epsilon-connected ordinal set
aStart . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal set
aStart . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal set
zz . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
S02 is epsilon-transitive epsilon-connected ordinal set
S01 . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S0max is epsilon-transitive epsilon-connected ordinal set
SS . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S0max is epsilon-transitive epsilon-connected ordinal set
SS . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
S02 is epsilon-transitive epsilon-connected ordinal set
S01 . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal set
A . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom IR is functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
field IR is set
CR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty functional finite set
{FIR} is non empty trivial functional finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is epsilon-transitive epsilon-connected ordinal set
zz . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is epsilon-transitive epsilon-connected ordinal set
FCR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is epsilon-transitive epsilon-connected ordinal set
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is epsilon-transitive epsilon-connected ordinal set
zz . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
CR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FIR is set
FCR is set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
A is set
zz is set
[A,zz] is V1() set
{A,zz} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is epsilon-transitive epsilon-connected ordinal set
Z . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is set
zz is set
[A,zz] is V1() set
{A,zz} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is epsilon-transitive epsilon-connected ordinal set
Z . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
CR is set
FIR is set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[FCR,A] is V1() set
{FCR,A} is non empty functional finite set
{FCR} is non empty trivial functional finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
bool R is non empty cup-closed diff-closed preBoolean set
support FCR is finite Element of bool R
support A is finite Element of bool R
(support FCR) \/ (support A) is finite Element of bool R
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
SgmX ((RelIncl R),((support FCR) \/ (support A))) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
dom FCR is Element of bool R
dom A is Element of bool R
field (RelIncl R) is set
rng (SgmX ((RelIncl R),((support FCR) \/ (support A)))) is finite set
dom (SgmX ((RelIncl R),((support FCR) \/ (support A)))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
len (SgmX ((RelIncl R),((support FCR) \/ (support A)))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz is set
A . ((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . ((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is set
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) . Z is set
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) . Z is set
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz is set
A . ((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . ((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z is epsilon-transitive epsilon-connected ordinal set
aStart is epsilon-transitive epsilon-connected ordinal set
SS is epsilon-transitive epsilon-connected ordinal set
A . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS is set
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS is epsilon-transitive epsilon-connected ordinal Element of R
(SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz is epsilon-transitive epsilon-connected ordinal Element of R
[((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)] is V1() set
{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)} is non empty finite set
{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)},{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. SS)}} is non empty finite V34() set
[((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)] is V1() set
{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)} is non empty finite set
{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) /. zz)},{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS)}} is non empty finite V34() set
[((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz)] is V1() set
{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz)} is non empty finite set
{{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS),((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . zz)},{((SgmX ((RelIncl R),((support FCR) \/ (support A)))) . SS)}} is non empty finite V34() set
A . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal set
A . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[A,FCR] is V1() set
{A,FCR} is non empty functional finite set
{A} is non empty trivial functional finite 1 -element set
{{A,FCR},{A}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal set
FCR . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[CR,FIR] is V1() set
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() set
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support CR is finite Element of bool R
SgmX ((RelIncl R),(support CR)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
rng (SgmX ((RelIncl R),(support CR))) is finite set
len (SgmX ((RelIncl R),(support CR))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (SgmX ((RelIncl R),(support CR))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
(SgmX ((RelIncl R),(support CR))) . (len (SgmX ((RelIncl R),(support CR)))) is set
FCR is epsilon-transitive epsilon-connected ordinal set
A is epsilon-transitive epsilon-connected ordinal set
CR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag R) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
(EmptyBag R) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),(support CR))) . zz is set
(SgmX ((RelIncl R),(support CR))) /. zz is epsilon-transitive epsilon-connected ordinal Element of R
(SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))) is epsilon-transitive epsilon-connected ordinal Element of R
[((SgmX ((RelIncl R),(support CR))) /. zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))] is V1() set
{((SgmX ((RelIncl R),(support CR))) /. zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))} is non empty finite set
{((SgmX ((RelIncl R),(support CR))) /. zz)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),(support CR))) /. zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))},{((SgmX ((RelIncl R),(support CR))) /. zz)}} is non empty finite V34() set
[((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))] is V1() set
{((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))} is non empty finite set
{((SgmX ((RelIncl R),(support CR))) . zz)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) /. (len (SgmX ((RelIncl R),(support CR)))))},{((SgmX ((RelIncl R),(support CR))) . zz)}} is non empty finite V34() set
[((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) . (len (SgmX ((RelIncl R),(support CR)))))] is V1() set
{((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) . (len (SgmX ((RelIncl R),(support CR)))))} is non empty finite set
{{((SgmX ((RelIncl R),(support CR))) . zz),((SgmX ((RelIncl R),(support CR))) . (len (SgmX ((RelIncl R),(support CR)))))},{((SgmX ((RelIncl R),(support CR))) . zz)}} is non empty finite V34() set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
A is epsilon-transitive epsilon-connected ordinal set
CR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(EmptyBag R) . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[CR,FIR] is V1() set
{CR,FIR} is non empty functional finite set
{CR} is non empty trivial functional finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
A is epsilon-transitive epsilon-connected ordinal set
FIR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(CR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR . zz) + (FCR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(FIR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(FIR . zz) + (FCR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is epsilon-transitive epsilon-connected ordinal set
(CR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR . zz) + (FCR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(FIR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FIR . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(FIR . zz) + (FCR . zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
zz is epsilon-transitive epsilon-connected ordinal set
(FIR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(CR + FCR) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[CR,FIR] is V1() set
{CR,FIR} is non empty functional finite set
{CR} is non empty trivial functional finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
field (R) is set
RelStr(# (Bags R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the InternalRel of RelStr(# (Bags R),(R) #) is Relation-like the carrier of RelStr(# (Bags R),(R) #) -defined the carrier of RelStr(# (Bags R),(R) #) -valued total V18( the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):]
the carrier of RelStr(# (Bags R),(R) #) is non empty set
[: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):] is non empty Relation-like set
bool [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):] is non empty cup-closed diff-closed preBoolean set
[:NAT, the carrier of RelStr(# (Bags R),(R) #):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of RelStr(# (Bags R),(R) #):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
FCR is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags R),(R) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags R),(R) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags R),(R) #):]
FCR . 0 is Element of the carrier of RelStr(# (Bags R),(R) #)
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support A is finite Element of bool R
bool R is non empty cup-closed diff-closed preBoolean set
RelIncl R is Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty cup-closed diff-closed preBoolean set
SgmX ((RelIncl R),(support A)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
field (RelIncl R) is set
rng (SgmX ((RelIncl R),(support A))) is finite set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FCR . (0 + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal set
A . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
len (SgmX ((RelIncl R),(support A))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
dom (SgmX ((RelIncl R),(support A))) is finite V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of bool NAT
(SgmX ((RelIncl R),(support A))) . (len (SgmX ((RelIncl R),(support A)))) is set
zz is epsilon-transitive epsilon-connected ordinal set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . Z is Element of the carrier of RelStr(# (Bags R),(R) #)
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . Z is set
Z is non empty Relation-like NAT -defined NAT -valued Function-like total V18( NAT , NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
aStart is epsilon-transitive epsilon-connected ordinal set
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(SgmX ((RelIncl R),(support A))) . SS is set
(SgmX ((RelIncl R),(support A))) /. SS is epsilon-transitive epsilon-connected ordinal Element of R
(SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))) is epsilon-transitive epsilon-connected ordinal Element of R
[((SgmX ((RelIncl R),(support A))) /. SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))] is V1() set
{((SgmX ((RelIncl R),(support A))) /. SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))} is non empty finite set
{((SgmX ((RelIncl R),(support A))) /. SS)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),(support A))) /. SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))},{((SgmX ((RelIncl R),(support A))) /. SS)}} is non empty finite V34() set
[((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))] is V1() set
{((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))} is non empty finite set
{((SgmX ((RelIncl R),(support A))) . SS)} is non empty trivial finite 1 -element set
{{((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) /. (len (SgmX ((RelIncl R),(support A)))))},{((SgmX ((RelIncl R),(support A))) . SS)}} is non empty finite V34() set
[((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) . (len (SgmX ((RelIncl R),(support A)))))] is V1() set
{((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) . (len (SgmX ((RelIncl R),(support A)))))} is non empty finite set
{{((SgmX ((RelIncl R),(support A))) . SS),((SgmX ((RelIncl R),(support A))) . (len (SgmX ((RelIncl R),(support A)))))},{((SgmX ((RelIncl R),(support A))) . SS)}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR . aStart is Element of the carrier of RelStr(# (Bags R),(R) #)
aStart + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FCR . (aStart + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
SS is epsilon-transitive epsilon-connected ordinal set
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S01 . SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[SS,S01] is V1() set
{SS,S01} is non empty functional finite set
{SS} is non empty trivial functional finite 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
S02 is epsilon-transitive epsilon-connected ordinal set
S01 . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
the carrier of OrderedNAT is non empty set
[:NAT, the carrier of OrderedNAT:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of OrderedNAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
aStart is non empty Relation-like NAT -defined the carrier of OrderedNAT -valued Function-like total V18( NAT , the carrier of OrderedNAT) Element of bool [:NAT, the carrier of OrderedNAT:]
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
aStart . (SS + 1) is Element of the carrier of OrderedNAT
aStart . SS is Element of the carrier of OrderedNAT
[(aStart . (SS + 1)),(aStart . SS)] is V1() Element of [: the carrier of OrderedNAT, the carrier of OrderedNAT:]
[: the carrier of OrderedNAT, the carrier of OrderedNAT:] is non empty Relation-like set
{(aStart . (SS + 1)),(aStart . SS)} is non empty finite set
{(aStart . (SS + 1))} is non empty trivial finite 1 -element set
{{(aStart . (SS + 1)),(aStart . SS)},{(aStart . (SS + 1))}} is non empty finite V34() set
the InternalRel of OrderedNAT is Relation-like the carrier of OrderedNAT -defined the carrier of OrderedNAT -valued Element of bool [: the carrier of OrderedNAT, the carrier of OrderedNAT:]
bool [: the carrier of OrderedNAT, the carrier of OrderedNAT:] is non empty cup-closed diff-closed preBoolean set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . SS is Element of the carrier of OrderedNAT
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
aStart . (SS + 1) is Element of the carrier of OrderedNAT
FCR . SS is Element of the carrier of RelStr(# (Bags R),(R) #)
FCR . (SS + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
a0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S0max is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[a0,S0max] is V1() set
{a0,S0max} is non empty functional finite set
{a0} is non empty trivial functional finite 1 -element set
{{a0,S0max},{a0}} is non empty finite V34() set
i0 is epsilon-transitive epsilon-connected ordinal set
S0max . i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a0 . i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b0t is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0t . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0 . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0t is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0t . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0 . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(zz) is Relation-like Bags zz -defined Bags zz -valued total V18( Bags zz, Bags zz) reflexive antisymmetric transitive (zz) Element of bool [:(Bags zz),(Bags zz):]
Bags zz is non empty functional Element of bool (Bags zz)
Bags zz is non empty set
bool (Bags zz) is non empty cup-closed diff-closed preBoolean set
[:(Bags zz),(Bags zz):] is non empty Relation-like set
bool [:(Bags zz),(Bags zz):] is non empty cup-closed diff-closed preBoolean set
RelStr(# (Bags zz),(zz) #) is non empty strict total reflexive transitive antisymmetric RelStr
field (zz) is set
S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
aStart . S02 is Element of the carrier of OrderedNAT
S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 + S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . (S02 + S0max) is Element of the carrier of RelStr(# (Bags R),(R) #)
a0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a0 | zz is Relation-like zz -defined R -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued finite-support set
i0 is Relation-like zz -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0t is Relation-like zz -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags zz
b0 is Relation-like zz -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags zz
S02 + S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR . (S02 + S0max) is Element of the carrier of RelStr(# (Bags R),(R) #)
[:NAT,(Bags zz):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Bags zz):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
S0max is non empty Relation-like NAT -defined Bags zz -valued Function-like total V18( NAT , Bags zz) Element of bool [:NAT,(Bags zz):]
the carrier of RelStr(# (Bags zz),(zz) #) is non empty set
[:NAT, the carrier of RelStr(# (Bags zz),(zz) #):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of RelStr(# (Bags zz),(zz) #):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 + i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR . (S02 + i0) is Element of the carrier of RelStr(# (Bags R),(R) #)
a0 is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags zz),(zz) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags zz),(zz) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags zz),(zz) #):]
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a0 . b0t is Element of the carrier of RelStr(# (Bags zz),(zz) #)
b0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0 | zz is Relation-like zz -defined R -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued finite-support set
i0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S02 + (i0 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FCR . (S02 + (i0 + 1)) is Element of the carrier of RelStr(# (Bags R),(R) #)
a0 . (i0 + 1) is Element of the carrier of RelStr(# (Bags zz),(zz) #)
S is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S | zz is Relation-like zz -defined R -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued finite-support set
(S02 + i0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S02 + b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . (S02 + b0t) is Element of the carrier of OrderedNAT
aStart . (S02 + (i0 + 1)) is Element of the carrier of OrderedNAT
aStart . (S02 + i0) is Element of the carrier of OrderedNAT
a0 . i0 is Element of the carrier of RelStr(# (Bags zz),(zz) #)
dom b0 is Element of bool R
dom S is Element of bool R
a is set
(b0 | zz) . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0 . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0 . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0 . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . ((S02 + i0) + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
[(FCR . ((S02 + i0) + 1)),(FCR . (S02 + i0))] is V1() Element of [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):]
{(FCR . ((S02 + i0) + 1)),(FCR . (S02 + i0))} is non empty finite set
{(FCR . ((S02 + i0) + 1))} is non empty trivial finite 1 -element set
{{(FCR . ((S02 + i0) + 1)),(FCR . (S02 + i0))},{(FCR . ((S02 + i0) + 1))}} is non empty finite V34() set
a is epsilon-transitive epsilon-connected ordinal set
b0 . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n is Relation-like zz -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a is Relation-like zz -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a . a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b is epsilon-transitive epsilon-connected ordinal set
b0 . b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
a . b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n . b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[(a0 . (i0 + 1)),(a0 . i0)] is V1() Element of [: the carrier of RelStr(# (Bags zz),(zz) #), the carrier of RelStr(# (Bags zz),(zz) #):]
[: the carrier of RelStr(# (Bags zz),(zz) #), the carrier of RelStr(# (Bags zz),(zz) #):] is non empty Relation-like set
{(a0 . (i0 + 1)),(a0 . i0)} is non empty finite set
{(a0 . (i0 + 1))} is non empty trivial finite 1 -element set
{{(a0 . (i0 + 1)),(a0 . i0)},{(a0 . (i0 + 1))}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
CR is Relation-like Bags R -defined Bags R -valued Element of bool [:(Bags R),(Bags R):]
FIR is set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
[(EmptyBag R),(EmptyBag R)] is V1() Element of [:(Bags R),(Bags R):]
{(EmptyBag R),(EmptyBag R)} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),(EmptyBag R)},{(EmptyBag R)}} is non empty finite V34() set
(EmptyBag R) + A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[((EmptyBag R) + A),((EmptyBag R) + A)] is V1() set
{((EmptyBag R) + A),((EmptyBag R) + A)} is non empty functional finite set
{((EmptyBag R) + A)} is non empty trivial functional finite 1 -element set
{{((EmptyBag R) + A),((EmptyBag R) + A)},{((EmptyBag R) + A)}} is non empty finite V34() set
[A,((EmptyBag R) + A)] is V1() set
{A,((EmptyBag R) + A)} is non empty functional finite set
{A} is non empty trivial functional finite 1 -element set
{{A,((EmptyBag R) + A)},{A}} is non empty finite V34() set
[A,A] is V1() set
{A,A} is non empty functional finite set
{{A,A},{A}} is non empty finite V34() set
[FIR,FIR] is V1() set
{FIR,FIR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FIR},{FIR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[A,A] is V1() set
{A,A} is non empty functional finite set
{A} is non empty trivial functional finite 1 -element set
{{A,A},{A}} is non empty finite V34() set
FIR is set
FCR is set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
[FCR,FIR] is V1() set
{FCR,FIR} is non empty finite set
{FCR} is non empty trivial finite 1 -element set
{{FCR,FIR},{FCR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[A,zz] is V1() set
{A,zz} is non empty functional finite set
{A} is non empty trivial functional finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,Z) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,Z] is V1() set
{zz,Z} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,Z) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,Z] is V1() set
{zz,Z} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
FIR is set
FCR is set
A is set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
[FCR,A] is V1() set
{FCR,A} is non empty finite set
{FCR} is non empty trivial finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,zz] is V1() set
{zz,zz} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,Z) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[Z,aStart] is V1() set
{Z,aStart} is non empty functional finite set
{Z} is non empty trivial functional finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,aStart},{zz}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,aStart},{zz}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,aStart},{zz}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty functional finite set
{{zz,aStart},{zz}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[zz,aStart] is V1() set
{zz,aStart} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,aStart},{zz}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
[FIR,A] is V1() set
{FIR,A} is non empty finite set
{{FIR,A},{FIR}} is non empty finite V34() set
dom CR is functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
field CR is set
FIR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[FCR,A] is V1() set
{FCR,A} is non empty functional finite set
{FCR} is non empty trivial functional finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
(R,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,zz] is V1() set
{zz,zz} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
CR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FIR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FCR is set
A is set
[FCR,A] is V1() set
{FCR,A} is non empty finite set
{FCR} is non empty trivial finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
dom CR is functional Element of bool (Bags R)
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
rng CR is functional Element of bool (Bags R)
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,zz] is V1() set
{zz,zz} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
dom FIR is functional Element of bool (Bags R)
rng FIR is functional Element of bool (Bags R)
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[zz,zz] is V1() set
{zz,zz} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
(R,IR) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
CR is set
FIR is set
[CR,FIR] is V1() set
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[FIR,CR] is V1() set
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
[FIR,CR] is V1() set
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,(EmptyBag R)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(EmptyBag R),CR] is V1() set
{(EmptyBag R),CR} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),CR},{(EmptyBag R)}} is non empty finite V34() set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[CR,FIR] is V1() set
{CR,FIR} is non empty functional finite set
{CR} is non empty trivial functional finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
(R,FIR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(CR + FCR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,CR) + (R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(FIR + FCR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FIR) + (R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FIR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(CR + FCR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,FIR) + (R,FCR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R,(FIR + FCR)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
(R,FIR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R,CR) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[CR,FIR] is V1() set
{CR,FIR} is non empty functional finite set
{CR} is non empty trivial functional finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR + FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(CR + FCR),(FIR + FCR)] is V1() set
{(CR + FCR),(FIR + FCR)} is non empty functional finite set
{(CR + FCR)} is non empty trivial functional finite 1 -element set
{{(CR + FCR),(FIR + FCR)},{(CR + FCR)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order (R) Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
(R,(BagOrder R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
(R,(R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order (R) Element of bool [:(Bags R),(Bags R):]
(R,(BagOrder R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[IR,CR] is V1() set
{IR,CR} is non empty functional finite set
{IR} is non empty trivial functional finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR + FIR),(CR + FIR)] is V1() set
{(IR + FIR),(CR + FIR)} is non empty functional finite set
{(IR + FIR)} is non empty trivial functional finite 1 -element set
{{(IR + FIR),(CR + FIR)},{(IR + FIR)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order (R) Element of bool [:(Bags R),(Bags R):]
(R,(BagOrder R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
R is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
BagOrder R is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive being_linear-order (R) Element of bool [:(Bags R),(Bags R):]
(R,(BagOrder R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
RelStr(# (Bags R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the InternalRel of RelStr(# (Bags R),(R) #) is Relation-like the carrier of RelStr(# (Bags R),(R) #) -defined the carrier of RelStr(# (Bags R),(R) #) -valued total V18( the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):]
the carrier of RelStr(# (Bags R),(R) #) is non empty set
[: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):] is non empty Relation-like set
bool [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):] is non empty cup-closed diff-closed preBoolean set
field the InternalRel of RelStr(# (Bags R),(R) #) is set
R --> 0 is non empty Relation-like R -defined NAT -valued RAT -valued INT -valued Function-like total V18(R, NAT ) T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
[:R,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:R,NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) +* (A,1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
dom (R --> 0) is non empty epsilon-transitive epsilon-connected ordinal Element of bool R
bool R is non empty non trivial non finite cup-closed diff-closed preBoolean set
Z is set
{A} is non empty trivial finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of bool NAT
zz is Relation-like R -defined Function-like total set
zz . Z is set
(R --> 0) . Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
support zz is set
Z is Element of the carrier of RelStr(# (Bags R),(R) #)
aStart is Element of the carrier of RelStr(# (Bags R),(R) #)
[:NAT, the carrier of RelStr(# (Bags R),(R) #):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of RelStr(# (Bags R),(R) #):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
A is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags R),(R) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags R),(R) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags R),(R) #):]
zz is non empty Relation-like NAT -defined the carrier of RelStr(# (Bags R),(R) #) -valued Function-like total V18( NAT , the carrier of RelStr(# (Bags R),(R) #)) Element of bool [:NAT, the carrier of RelStr(# (Bags R),(R) #):]
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
zz . (zz + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
zz . zz is Element of the carrier of RelStr(# (Bags R),(R) #)
[(zz . (zz + 1)),(zz . zz)] is V1() set
{(zz . (zz + 1)),(zz . zz)} is non empty finite set
{(zz . (zz + 1))} is non empty trivial finite 1 -element set
{{(zz . (zz + 1)),(zz . zz)},{(zz . (zz + 1))}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
zz . (Z + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
zz . Z is Element of the carrier of RelStr(# (Bags R),(R) #)
(R --> 0) +* ((zz + 1),1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
(R --> 0) +* (zz,1) is non empty Relation-like R -defined NAT -valued RAT -valued Function-like total V18(R, NAT ) complex-valued ext-real-valued real-valued natural-valued Element of bool [:R,NAT:]
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S01 . zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 is epsilon-transitive epsilon-connected ordinal set
{ b1 where b1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT : not Z + 1 <= b1 } is set
SS . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . (zz + 1) is Element of the carrier of RelStr(# (Bags R),(R) #)
[(zz . (zz + 1)),(zz . zz)] is V1() Element of [: the carrier of RelStr(# (Bags R),(R) #), the carrier of RelStr(# (Bags R),(R) #):]
{(zz . (zz + 1)),(zz . zz)} is non empty finite set
{(zz . (zz + 1))} is non empty trivial finite 1 -element set
{{(zz . (zz + 1)),(zz . zz)},{(zz . (zz + 1))}} is non empty finite V34() set
(R,S01) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
support S01 is finite Element of bool R
RelIncl R is non empty Relation-like R -defined R -valued total V18(R,R) reflexive antisymmetric connected transitive well_founded well-ordering Element of bool [:R,R:]
[:R,R:] is non empty non trivial Relation-like non finite set
bool [:R,R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
SgmX ((RelIncl R),(support S01)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
S01 * (SgmX ((RelIncl R),(support S01))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
S02 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R,SS) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
support SS is finite Element of bool R
SgmX ((RelIncl R),(support SS)) is Relation-like NAT -defined R -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of R
SS * (SgmX ((RelIncl R),(support SS))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
S0max is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Cardinal-yielding finite-support FinSequence of NAT
Sum S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
field (RelIncl R) is set
b0t is set
i0 is epsilon-transitive epsilon-connected ordinal Element of R
SS . b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
{i0} is non empty trivial finite 1 -element Element of bool R
<*i0*> is non empty trivial Relation-like NAT -defined R -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of R
dom S01 is Element of bool R
dom SS is Element of bool R
b0t is set
a0 is epsilon-transitive epsilon-connected ordinal Element of R
S01 . b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(R --> 0) . b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
{a0} is non empty trivial finite 1 -element Element of bool R
<*a0*> is non empty trivial Relation-like NAT -defined R -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of R
<*(S01 . zz)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V66() decreasing non-decreasing non-increasing Cardinal-yielding finite-support FinSequence of NAT
<*1*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V66() decreasing non-decreasing non-increasing Cardinal-yielding finite-support FinSequence of NAT
SS . i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
<*(SS . i0)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V66() decreasing non-decreasing non-increasing Cardinal-yielding finite-support FinSequence of NAT
b0t is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[b0t,b0] is V1() set
{b0t,b0} is non empty functional finite set
{b0t} is non empty trivial functional finite 1 -element set
{{b0t,b0},{b0t}} is non empty finite V34() set
S is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0t + S is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b0 + S is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(b0t + S),(b0 + S)] is V1() set
{(b0t + S),(b0 + S)} is non empty functional finite set
{(b0t + S)} is non empty trivial functional finite 1 -element set
{{(b0t + S),(b0 + S)},{(b0t + S)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
(R,(R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
IR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[IR,CR] is V1() set
{IR,CR} is non empty functional finite set
{IR} is non empty trivial functional finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CR + FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR + FIR),(CR + FIR)] is V1() set
{(IR + FIR),(CR + FIR)} is non empty functional finite set
{(IR + FIR)} is non empty trivial functional finite 1 -element set
{{(IR + FIR),(CR + FIR)},{(IR + FIR)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
(R,(R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
R is epsilon-transitive epsilon-connected ordinal set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive (R) Element of bool [:(Bags R),(Bags R):]
(R,(R)) is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
field (R) is set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty functional finite set
{FIR} is non empty trivial functional finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FIR + A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
FCR + A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(FIR + A),(FCR + A)] is V1() set
{(FIR + A),(FCR + A)} is non empty functional finite set
{(FIR + A)} is non empty trivial functional finite 1 -element set
{{(FIR + A),(FCR + A)},{(FIR + A)}} is non empty finite V34() set
FIR is set
{ (R,b1) where b1 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R : b1 in FIR } is set
A is set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,zz) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,Z) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
min zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
{ b1 where b1 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R : ( b1 in FIR & (R,b1) = min zz ) } is set
aStart is set
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,SS) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
field (R) is set
SS is set
(R) -Seg SS is set
((R) -Seg SS) /\ { b1 where b1 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R : ( b1 in FIR & (R,b1) = min zz ) } is set
SS is set
S01 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S01) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R) -Seg SS is set
((R) -Seg SS) /\ FIR is set
S01 is set
[S01,SS] is V1() set
{S01,SS} is non empty finite set
{S01} is non empty trivial finite 1 -element set
{{S01,SS},{S01}} is non empty finite V34() set
a0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,a0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S02) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S0max) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
a0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,a0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S0max) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S02) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
[S0max,S02] is V1() Element of [:(Bags R),(Bags R):]
{S0max,S02} is non empty functional finite set
{S0max} is non empty trivial functional finite 1 -element set
{{S0max,S02},{S0max}} is non empty finite V34() set
(R) -Seg S02 is set
a0 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,a0) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S0max) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S02) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S02) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
(R,S0max) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
Bags (R + 1) is non empty functional Element of bool (Bags (R + 1))
Bags (R + 1) is non empty set
bool (Bags (R + 1)) is non empty cup-closed diff-closed preBoolean set
[:(Bags (R + 1)),(Bags (R + 1)):] is non empty Relation-like set
bool [:(Bags (R + 1)),(Bags (R + 1)):] is non empty cup-closed diff-closed preBoolean set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR -' (R + 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Bags (IR -' (R + 1)) is non empty functional Element of bool (Bags (IR -' (R + 1)))
Bags (IR -' (R + 1)) is non empty set
bool (Bags (IR -' (R + 1))) is non empty cup-closed diff-closed preBoolean set
[:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):] is non empty Relation-like set
bool [:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):] is non empty cup-closed diff-closed preBoolean set
Bags IR is non empty functional Element of bool (Bags IR)
Bags IR is non empty set
bool (Bags IR) is non empty cup-closed diff-closed preBoolean set
[:(Bags IR),(Bags IR):] is non empty Relation-like set
bool [:(Bags IR),(Bags IR):] is non empty cup-closed diff-closed preBoolean set
CR is Relation-like Bags (R + 1) -defined Bags (R + 1) -valued total V18( Bags (R + 1), Bags (R + 1)) reflexive antisymmetric transitive Element of bool [:(Bags (R + 1)),(Bags (R + 1)):]
FIR is Relation-like Bags (IR -' (R + 1)) -defined Bags (IR -' (R + 1)) -valued total V18( Bags (IR -' (R + 1)), Bags (IR -' (R + 1))) reflexive antisymmetric transitive Element of bool [:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):]
(R + 1) -' 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR is Relation-like Bags IR -defined Bags IR -valued Element of bool [:(Bags IR),(Bags IR):]
A is set
zz is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),zz) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,zz) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
[A,A] is V1() set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V34() set
A is set
zz is set
[A,zz] is V1() set
{A,zz} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
zz is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),zz) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)] is V1() set
{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)} is non empty functional finite set
{(IR,0,(R + 1),zz)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)},{(IR,0,(R + 1),zz)}} is non empty finite V34() set
(IR,(R + 1),IR,zz) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
Bags ((R + 1) -' 0) is non empty functional Element of bool (Bags ((R + 1) -' 0))
Bags ((R + 1) -' 0) is non empty set
bool (Bags ((R + 1) -' 0)) is non empty cup-closed diff-closed preBoolean set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
S02 is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S0max is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),S02) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),S0max) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)] is V1() set
{(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)} is non empty functional finite set
{(IR,0,(R + 1),S02)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)},{(IR,0,(R + 1),S02)}} is non empty finite V34() set
(IR,(R + 1),IR,S02) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,S0max) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)] is V1() set
{(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)} is non empty functional finite set
{(IR,(R + 1),IR,S02)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)},{(IR,(R + 1),IR,S02)}} is non empty finite V34() set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
S02 is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S0max is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),S02) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),S0max) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)] is V1() set
{(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)} is non empty functional finite set
{(IR,0,(R + 1),S02)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),S02),(IR,0,(R + 1),S0max)},{(IR,0,(R + 1),S02)}} is non empty finite V34() set
(IR,(R + 1),IR,S02) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,S0max) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)] is V1() set
{(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)} is non empty functional finite set
{(IR,(R + 1),IR,S02)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,S02),(IR,(R + 1),IR,S0max)},{(IR,(R + 1),IR,S02)}} is non empty finite V34() set
A is set
zz is set
zz is set
[A,zz] is V1() set
{A,zz} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
[zz,zz] is V1() set
{zz,zz} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),aStart) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,aStart) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
SS is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),SS) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),SS) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),SS)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),SS)}} is non empty finite V34() set
(IR,(R + 1),IR,SS) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,SS) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,SS)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,SS)}} is non empty finite V34() set
[(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),aStart)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),aStart)}} is non empty finite V34() set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),SS)} is non empty functional finite set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,aStart)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,aStart)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),aStart)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),aStart)}} is non empty finite V34() set
[(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,aStart)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,aStart)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),aStart)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),aStart)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,aStart)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,aStart)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,SS)} is non empty functional finite set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),aStart)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),aStart),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),aStart)}} is non empty finite V34() set
[(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,aStart)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,aStart),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,aStart)}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
[A,zz] is V1() set
{A,zz} is non empty finite set
{{A,zz},{A}} is non empty finite V34() set
dom FCR is functional Element of bool (Bags IR)
bool (Bags IR) is non empty cup-closed diff-closed preBoolean set
field FCR is set
A is Relation-like Bags IR -defined Bags IR -valued total V18( Bags IR, Bags IR) reflexive antisymmetric transitive Element of bool [:(Bags IR),(Bags IR):]
zz is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[zz,zz] is V1() set
{zz,zz} is non empty functional finite set
{zz} is non empty trivial functional finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
(IR,0,(R + 1),zz) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),zz) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),zz),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),zz),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),zz)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),zz),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),zz)}} is non empty finite V34() set
(IR,(R + 1),IR,zz) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,zz) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),aStart) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,aStart) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
FCR is Relation-like Bags IR -defined Bags IR -valued total V18( Bags IR, Bags IR) reflexive antisymmetric transitive Element of bool [:(Bags IR),(Bags IR):]
A is Relation-like Bags IR -defined Bags IR -valued total V18( Bags IR, Bags IR) reflexive antisymmetric transitive Element of bool [:(Bags IR),(Bags IR):]
zz is set
zz is set
[zz,zz] is V1() set
{zz,zz} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
dom FCR is functional Element of bool (Bags IR)
bool (Bags IR) is non empty cup-closed diff-closed preBoolean set
rng FCR is functional Element of bool (Bags IR)
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(R + 1) -' 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),aStart) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,aStart) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
dom A is functional Element of bool (Bags IR)
rng A is functional Element of bool (Bags IR)
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),aStart) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),aStart)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,aStart) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,aStart)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
Bags (R + 1) is non empty functional Element of bool (Bags (R + 1))
Bags (R + 1) is non empty set
bool (Bags (R + 1)) is non empty cup-closed diff-closed preBoolean set
[:(Bags (R + 1)),(Bags (R + 1)):] is non empty Relation-like set
bool [:(Bags (R + 1)),(Bags (R + 1)):] is non empty cup-closed diff-closed preBoolean set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR -' (R + 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Bags (IR -' (R + 1)) is non empty functional Element of bool (Bags (IR -' (R + 1)))
Bags (IR -' (R + 1)) is non empty set
bool (Bags (IR -' (R + 1))) is non empty cup-closed diff-closed preBoolean set
[:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):] is non empty Relation-like set
bool [:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):] is non empty cup-closed diff-closed preBoolean set
CR is Relation-like Bags (R + 1) -defined Bags (R + 1) -valued total V18( Bags (R + 1), Bags (R + 1)) reflexive antisymmetric transitive Element of bool [:(Bags (R + 1)),(Bags (R + 1)):]
FIR is Relation-like Bags (IR -' (R + 1)) -defined Bags (IR -' (R + 1)) -valued total V18( Bags (IR -' (R + 1)), Bags (IR -' (R + 1))) reflexive antisymmetric transitive Element of bool [:(Bags (IR -' (R + 1))),(Bags (IR -' (R + 1))):]
(R,IR,CR,FIR) is Relation-like Bags IR -defined Bags IR -valued total V18( Bags IR, Bags IR) reflexive antisymmetric transitive Element of bool [:(Bags IR),(Bags IR):]
Bags IR is non empty functional Element of bool (Bags IR)
Bags IR is non empty set
bool (Bags IR) is non empty cup-closed diff-closed preBoolean set
[:(Bags IR),(Bags IR):] is non empty Relation-like set
bool [:(Bags IR),(Bags IR):] is non empty cup-closed diff-closed preBoolean set
(R + 1) -' 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Bags ((R + 1) -' 0) is non empty functional Element of bool (Bags ((R + 1) -' 0))
Bags ((R + 1) -' 0) is non empty set
bool (Bags ((R + 1) -' 0)) is non empty cup-closed diff-closed preBoolean set
A is set
zz is set
zz is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),zz) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,zz) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Z is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),Z) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,Z) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[A,zz] is V1() set
{A,zz} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,zz},{A}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)] is V1() set
{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)} is non empty functional finite set
{(IR,0,(R + 1),zz)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)},{(IR,0,(R + 1),zz)}} is non empty finite V34() set
[(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)] is V1() set
{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)} is non empty functional finite set
{(IR,0,(R + 1),Z)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),Z),(IR,0,(R + 1),zz)},{(IR,0,(R + 1),Z)}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
[(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)] is V1() set
{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)} is non empty functional finite set
{(IR,(R + 1),IR,Z)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,Z),(IR,(R + 1),IR,zz)},{(IR,(R + 1),IR,Z)}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)] is V1() set
{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)} is non empty functional finite set
{(IR,(R + 1),IR,zz)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,zz),(IR,(R + 1),IR,Z)},{(IR,(R + 1),IR,zz)}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[zz,A] is V1() set
{zz,A} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,A},{zz}} is non empty finite V34() set
[(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)] is V1() set
{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)} is non empty functional finite set
{(IR,0,(R + 1),zz)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),zz),(IR,0,(R + 1),Z)},{(IR,0,(R + 1),zz)}} is non empty finite V34() set
EmptyBag IR is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags IR
(IR,0,(R + 1),(EmptyBag IR)) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),A) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,(EmptyBag IR)) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,A) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
EmptyBag ((R + 1) -' 0) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags ((R + 1) -' 0)
[(IR,0,(R + 1),(EmptyBag IR)),(IR,0,(R + 1),A)] is V1() set
{(IR,0,(R + 1),(EmptyBag IR)),(IR,0,(R + 1),A)} is non empty functional finite set
{(IR,0,(R + 1),(EmptyBag IR))} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),(EmptyBag IR)),(IR,0,(R + 1),A)},{(IR,0,(R + 1),(EmptyBag IR))}} is non empty finite V34() set
[(EmptyBag IR),A] is V1() set
{(EmptyBag IR),A} is non empty functional finite set
{(EmptyBag IR)} is non empty trivial functional finite 1 -element set
{{(EmptyBag IR),A},{(EmptyBag IR)}} is non empty finite V34() set
EmptyBag (IR -' (R + 1)) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (IR -' (R + 1))
[(IR,(R + 1),IR,(EmptyBag IR)),(IR,(R + 1),IR,A)] is V1() set
{(IR,(R + 1),IR,(EmptyBag IR)),(IR,(R + 1),IR,A)} is non empty functional finite set
{(IR,(R + 1),IR,(EmptyBag IR))} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,(EmptyBag IR)),(IR,(R + 1),IR,A)},{(IR,(R + 1),IR,(EmptyBag IR))}} is non empty finite V34() set
[(EmptyBag IR),A] is V1() set
{(EmptyBag IR),A} is non empty functional finite set
{(EmptyBag IR)} is non empty trivial functional finite 1 -element set
{{(EmptyBag IR),A},{(EmptyBag IR)}} is non empty finite V34() set
[(EmptyBag IR),A] is V1() set
{(EmptyBag IR),A} is non empty functional finite set
{(EmptyBag IR)} is non empty trivial functional finite 1 -element set
{{(EmptyBag IR),A},{(EmptyBag IR)}} is non empty finite V34() set
[(EmptyBag IR),A] is V1() set
{(EmptyBag IR),A} is non empty functional finite set
{(EmptyBag IR)} is non empty trivial functional finite 1 -element set
{{(EmptyBag IR),A},{(EmptyBag IR)}} is non empty finite V34() set
SS is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[SS,SS] is V1() set
{SS,SS} is non empty functional finite set
{SS} is non empty trivial functional finite 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
(IR,0,(R + 1),SS) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,SS) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),SS) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,SS) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
S01 is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),S01) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,S01) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS + S01 is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),(SS + S01)) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS + S01 is Relation-like IR -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),(SS + S01)) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,(SS + S01)) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,(SS + S01)) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),SS)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),SS)}} is non empty finite V34() set
(IR,0,(R + 1),SS) + (IR,0,(R + 1),S01) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,0,(R + 1),SS) + (IR,0,(R + 1),S01) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))] is V1() set
{((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))} is non empty functional finite set
{((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))} is non empty trivial functional finite 1 -element set
{{((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))},{((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))}} is non empty finite V34() set
[(IR,0,(R + 1),(SS + S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))] is V1() set
{(IR,0,(R + 1),(SS + S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))} is non empty functional finite set
{(IR,0,(R + 1),(SS + S01))} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),(SS + S01)),((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01))},{(IR,0,(R + 1),(SS + S01))}} is non empty finite V34() set
[(IR,0,(R + 1),(SS + S01)),(IR,0,(R + 1),(SS + S01))] is V1() set
{(IR,0,(R + 1),(SS + S01)),(IR,0,(R + 1),(SS + S01))} is non empty functional finite set
{{(IR,0,(R + 1),(SS + S01)),(IR,0,(R + 1),(SS + S01))},{(IR,0,(R + 1),(SS + S01))}} is non empty finite V34() set
((IR,0,(R + 1),SS) + (IR,0,(R + 1),S01)) -' (IR,0,(R + 1),S01) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(SS + S01),(SS + S01)] is V1() set
{(SS + S01),(SS + S01)} is non empty functional finite set
{(SS + S01)} is non empty trivial functional finite 1 -element set
{{(SS + S01),(SS + S01)},{(SS + S01)}} is non empty finite V34() set
[(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,SS)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,SS)}} is non empty finite V34() set
(IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01) is Relation-like IR -' (R + 1) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))] is V1() set
{((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))} is non empty functional finite set
{((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))} is non empty trivial functional finite 1 -element set
{{((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))},{((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))}} is non empty finite V34() set
[(IR,(R + 1),IR,(SS + S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))] is V1() set
{(IR,(R + 1),IR,(SS + S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))} is non empty functional finite set
{(IR,(R + 1),IR,(SS + S01))} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,(SS + S01)),((IR,(R + 1),IR,SS) + (IR,(R + 1),IR,S01))},{(IR,(R + 1),IR,(SS + S01))}} is non empty finite V34() set
[(IR,(R + 1),IR,(SS + S01)),(IR,(R + 1),IR,(SS + S01))] is V1() set
{(IR,(R + 1),IR,(SS + S01)),(IR,(R + 1),IR,(SS + S01))} is non empty functional finite set
{{(IR,(R + 1),IR,(SS + S01)),(IR,(R + 1),IR,(SS + S01))},{(IR,(R + 1),IR,(SS + S01))}} is non empty finite V34() set
(IR,0,(R + 1),SS) + (IR,0,(R + 1),S01) is Relation-like (R + 1) -' 0 -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[(SS + S01),(SS + S01)] is V1() set
{(SS + S01),(SS + S01)} is non empty functional finite set
{(SS + S01)} is non empty trivial functional finite 1 -element set
{{(SS + S01),(SS + S01)},{(SS + S01)}} is non empty finite V34() set
[(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)] is V1() set
{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)} is non empty functional finite set
{(IR,0,(R + 1),SS)} is non empty trivial functional finite 1 -element set
{{(IR,0,(R + 1),SS),(IR,0,(R + 1),SS)},{(IR,0,(R + 1),SS)}} is non empty finite V34() set
[(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)] is V1() set
{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)} is non empty functional finite set
{(IR,(R + 1),IR,SS)} is non empty trivial functional finite 1 -element set
{{(IR,(R + 1),IR,SS),(IR,(R + 1),IR,SS)},{(IR,(R + 1),IR,SS)}} is non empty finite V34() set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like Bags R -defined Bags R -valued Element of bool [:(Bags R),(Bags R):]
RelStr(# (Bags R),IR #) is non empty strict RelStr
FIR is strict RelStr
the carrier of FIR is set
the InternalRel of FIR is Relation-like the carrier of FIR -defined the carrier of FIR -valued Element of bool [: the carrier of FIR, the carrier of FIR:]
[: the carrier of FIR, the carrier of FIR:] is Relation-like set
bool [: the carrier of FIR, the carrier of FIR:] is non empty cup-closed diff-closed preBoolean set
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
A is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[FCR,A] is V1() set
{FCR,A} is non empty functional finite set
{FCR} is non empty trivial functional finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
IR is strict RelStr
the carrier of IR is set
the InternalRel of IR is Relation-like the carrier of IR -defined the carrier of IR -valued Element of bool [: the carrier of IR, the carrier of IR:]
[: the carrier of IR, the carrier of IR:] is Relation-like set
bool [: the carrier of IR, the carrier of IR:] is non empty cup-closed diff-closed preBoolean set
CR is strict RelStr
the carrier of CR is set
the InternalRel of CR is Relation-like the carrier of CR -defined the carrier of CR -valued Element of bool [: the carrier of CR, the carrier of CR:]
[: the carrier of CR, the carrier of CR:] is Relation-like set
bool [: the carrier of CR, the carrier of CR:] is non empty cup-closed diff-closed preBoolean set
FIR is set
FCR is set
[FIR,FCR] is V1() set
{FIR,FCR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,FCR},{FIR}} is non empty finite V34() set
zz is set
zz is set
[zz,zz] is V1() set
{zz,zz} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
zz is set
Z is set
[zz,Z] is V1() set
{zz,Z} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
R --> OrderedNAT is Relation-like R -defined {OrderedNAT} -valued Function-like total V18(R,{OrderedNAT}) T-Sequence-like finite V125() V179() finite-support Element of bool [:R,{OrderedNAT}:]
{OrderedNAT} is non empty trivial finite 1 -element set
[:R,{OrderedNAT}:] is Relation-like finite set
bool [:R,{OrderedNAT}:] is non empty finite V34() cup-closed diff-closed preBoolean set
product (R --> OrderedNAT) is strict RelStr
the carrier of (product (R --> OrderedNAT)) is set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
Carrier (R --> OrderedNAT) is Relation-like R -defined Function-like total finite-support set
product (Carrier (R --> OrderedNAT)) is set
CR is set
dom (Carrier (R --> OrderedNAT)) is finite Element of bool R
bool R is non empty finite V34() cup-closed diff-closed preBoolean set
FIR is Relation-like Function-like set
dom FIR is set
rng FIR is set
FCR is set
A is set
FIR . A is set
(Carrier (R --> OrderedNAT)) . A is set
(R --> OrderedNAT) . A is set
zz is 1-sorted
the carrier of zz is set
FIR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
dom FIR is finite Element of bool R
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
dom FCR is finite Element of bool R
A is set
(R --> OrderedNAT) . A is set
(Carrier (R --> OrderedNAT)) . A is set
zz is 1-sorted
the carrier of zz is set
FCR . A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
dom FCR is finite Element of bool R
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(R) is strict RelStr
R --> OrderedNAT is Relation-like R -defined {OrderedNAT} -valued Function-like total V18(R,{OrderedNAT}) T-Sequence-like finite V125() V179() finite-support Element of bool [:R,{OrderedNAT}:]
{OrderedNAT} is non empty trivial finite 1 -element set
[:R,{OrderedNAT}:] is Relation-like finite set
bool [:R,{OrderedNAT}:] is non empty finite V34() cup-closed diff-closed preBoolean set
product (R --> OrderedNAT) is strict RelStr
the carrier of (R) is set
the InternalRel of (R) is Relation-like the carrier of (R) -defined the carrier of (R) -valued Element of bool [: the carrier of (R), the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is Relation-like set
bool [: the carrier of (R), the carrier of (R):] is non empty cup-closed diff-closed preBoolean set
the carrier of (product (R --> OrderedNAT)) is set
the InternalRel of (product (R --> OrderedNAT)) is Relation-like the carrier of (product (R --> OrderedNAT)) -defined the carrier of (product (R --> OrderedNAT)) -valued Element of bool [: the carrier of (product (R --> OrderedNAT)), the carrier of (product (R --> OrderedNAT)):]
[: the carrier of (product (R --> OrderedNAT)), the carrier of (product (R --> OrderedNAT)):] is Relation-like set
bool [: the carrier of (product (R --> OrderedNAT)), the carrier of (product (R --> OrderedNAT)):] is non empty cup-closed diff-closed preBoolean set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
zz is set
zz is set
[zz,zz] is V1() set
{zz,zz} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
dom the InternalRel of (R) is Element of bool the carrier of (R)
bool the carrier of (R) is non empty cup-closed diff-closed preBoolean set
rng the InternalRel of (R) is Element of bool the carrier of (R)
Z is Element of the carrier of (product (R --> OrderedNAT))
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
IR --> OrderedNAT is Relation-like IR -defined {OrderedNAT} -valued Function-like total V18(IR,{OrderedNAT}) T-Sequence-like finite V125() V179() finite-support Element of bool [:IR,{OrderedNAT}:]
[:IR,{OrderedNAT}:] is Relation-like finite set
bool [:IR,{OrderedNAT}:] is non empty finite V34() cup-closed diff-closed preBoolean set
product (IR --> OrderedNAT) is non empty strict antisymmetric quasi_ordered Dickson RelStr
the carrier of (product (IR --> OrderedNAT)) is non empty set
Carrier (R --> OrderedNAT) is Relation-like R -defined Function-like total finite-support set
product (Carrier (R --> OrderedNAT)) is set
aStart is Element of the carrier of (product (R --> OrderedNAT))
S01 is Relation-like Function-like set
S02 is Relation-like Function-like set
S0max is Relation-like Function-like set
a0 is Relation-like Function-like set
i0 is set
(R --> OrderedNAT) . i0 is set
b0 is RelStr
S0max . i0 is set
a0 . i0 is set
dom S0max is set
rng S0max is set
dom a0 is set
rng a0 is set
S is RelStr
the carrier of S is set
n is Element of the carrier of S
b is Element of the carrier of S
i is Element of the carrier of S
n1 is Element of the carrier of S
n1 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Sn12 is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n1 . i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Sn12 . i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[i,n1] is V1() set
{i,n1} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,n1},{i}} is non empty finite V34() set
SS is Relation-like Function-like set
SS is Relation-like Function-like set
dom the InternalRel of (product (R --> OrderedNAT)) is Element of bool the carrier of (product (R --> OrderedNAT))
bool the carrier of (product (R --> OrderedNAT)) is non empty cup-closed diff-closed preBoolean set
rng the InternalRel of (product (R --> OrderedNAT)) is Element of bool the carrier of (product (R --> OrderedNAT))
Z is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
SS is Element of the carrier of (product (R --> OrderedNAT))
SS is Element of the carrier of (product (R --> OrderedNAT))
S01 is Relation-like Function-like set
S02 is Relation-like Function-like set
S0max is set
(R --> OrderedNAT) . S0max is set
S01 . S0max is set
S02 . S0max is set
a0 is RelStr
the carrier of a0 is set
i0 is Element of the carrier of a0
b0t is Element of the carrier of a0
[i0,b0t] is V1() set
{i0,b0t} is non empty finite set
{i0} is non empty trivial finite 1 -element set
{{i0,b0t},{i0}} is non empty finite V34() set
b0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
[b0,S] is V1() Element of [:NAT,NAT:]
{b0,S} is non empty finite V34() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
{b0} is non empty trivial finite V34() 1 -element V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() set
{{b0,S},{b0}} is non empty finite V34() set
Z . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart . S0max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Bags R is non empty functional Element of bool (Bags R)
Bags R is non empty set
bool (Bags R) is non empty cup-closed diff-closed preBoolean set
[:(Bags R),(Bags R):] is non empty Relation-like set
bool [:(Bags R),(Bags R):] is non empty cup-closed diff-closed preBoolean set
(R) is strict RelStr
the carrier of (R) is set
the InternalRel of (R) is Relation-like the carrier of (R) -defined the carrier of (R) -valued Element of bool [: the carrier of (R), the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is Relation-like set
bool [: the carrier of (R), the carrier of (R):] is non empty cup-closed diff-closed preBoolean set
IR is Relation-like Bags R -defined Bags R -valued total V18( Bags R, Bags R) reflexive antisymmetric transitive Element of bool [:(Bags R),(Bags R):]
FCR is set
A is set
[FCR,A] is V1() set
{FCR,A} is non empty finite set
{FCR} is non empty trivial finite 1 -element set
{{FCR,A},{FCR}} is non empty finite V34() set
dom the InternalRel of (R) is Element of bool the carrier of (R)
bool the carrier of (R) is non empty cup-closed diff-closed preBoolean set
rng the InternalRel of (R) is Element of bool the carrier of (R)
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
zz -' zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
aStart is set
(zz -' zz) + zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
((zz -' zz) + zz) . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(zz -' zz) . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
((zz -' zz) . aStart) + (zz . aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz . aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(zz . aStart) -' (zz . aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
((zz . aStart) -' (zz . aStart)) + (zz . aStart) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(zz . aStart) - (zz . aStart) is V42() V43() ext-real Element of REAL
(zz . aStart) - (zz . aStart) is V42() V43() ext-real Element of REAL
- (zz . aStart) is V42() V43() ext-real non positive Element of REAL
(zz . aStart) + (- (zz . aStart)) is V42() V43() ext-real Element of REAL
((zz . aStart) + (- (zz . aStart))) + (zz . aStart) is V42() V43() ext-real Element of REAL
EmptyBag R is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags R
[(EmptyBag R),(zz -' zz)] is V1() set
{(EmptyBag R),(zz -' zz)} is non empty functional finite set
{(EmptyBag R)} is non empty trivial functional finite 1 -element set
{{(EmptyBag R),(zz -' zz)},{(EmptyBag R)}} is non empty finite V34() set
(EmptyBag R) + zz is Relation-like R -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
[((EmptyBag R) + zz),((zz -' zz) + zz)] is V1() set
{((EmptyBag R) + zz),((zz -' zz) + zz)} is non empty functional finite set
{((EmptyBag R) + zz)} is non empty trivial functional finite 1 -element set
{{((EmptyBag R) + zz),((zz -' zz) + zz)},{((EmptyBag R) + zz)}} is non empty finite V34() set
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
CR --> OrderedNAT is Relation-like CR -defined {OrderedNAT} -valued Function-like total V18(CR,{OrderedNAT}) T-Sequence-like finite V125() V179() finite-support Element of bool [:CR,{OrderedNAT}:]
{OrderedNAT} is non empty trivial finite 1 -element set
[:CR,{OrderedNAT}:] is Relation-like finite set
bool [:CR,{OrderedNAT}:] is non empty finite V34() cup-closed diff-closed preBoolean set
product (CR --> OrderedNAT) is non empty strict antisymmetric quasi_ordered Dickson RelStr
RelStr(# (Bags R),IR #) is non empty strict total reflexive transitive antisymmetric RelStr
the carrier of (product (CR --> OrderedNAT)) is non empty set
the InternalRel of (product (CR --> OrderedNAT)) is Relation-like the carrier of (product (CR --> OrderedNAT)) -defined the carrier of (product (CR --> OrderedNAT)) -valued Element of bool [: the carrier of (product (CR --> OrderedNAT)), the carrier of (product (CR --> OrderedNAT)):]
[: the carrier of (product (CR --> OrderedNAT)), the carrier of (product (CR --> OrderedNAT)):] is non empty Relation-like set
bool [: the carrier of (product (CR --> OrderedNAT)), the carrier of (product (CR --> OrderedNAT)):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of RelStr(# (Bags R),IR #) is Relation-like the carrier of RelStr(# (Bags R),IR #) -defined the carrier of RelStr(# (Bags R),IR #) -valued total V18( the carrier of RelStr(# (Bags R),IR #), the carrier of RelStr(# (Bags R),IR #)) reflexive antisymmetric transitive Element of bool [: the carrier of RelStr(# (Bags R),IR #), the carrier of RelStr(# (Bags R),IR #):]
the carrier of RelStr(# (Bags R),IR #) is non empty set
[: the carrier of RelStr(# (Bags R),IR #), the carrier of RelStr(# (Bags R),IR #):] is non empty Relation-like set
bool [: the carrier of RelStr(# (Bags R),IR #), the carrier of RelStr(# (Bags R),IR #):] is non empty cup-closed diff-closed preBoolean set
RelStr(# (Bags R),IR #) \~ is non empty strict transitive antisymmetric RelStr
field IR is set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
IR is finite Element of Fin the carrier of R
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
FIR is Element of the carrier of R
CR is Element of the carrier of R
FIR is Element of the carrier of R
[CR,FIR] is V1() Element of [: the carrier of R, the carrier of R:]
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() Element of [: the carrier of R, the carrier of R:]
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
[CR,FIR] is V1() Element of [: the carrier of R, the carrier of R:]
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() Element of [: the carrier of R, the carrier of R:]
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
FIR is Element of the carrier of R
CR is Element of the carrier of R
FIR is Element of the carrier of R
[CR,FIR] is V1() Element of [: the carrier of R, the carrier of R:]
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() Element of [: the carrier of R, the carrier of R:]
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
[CR,FIR] is V1() Element of [: the carrier of R, the carrier of R:]
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
[FIR,CR] is V1() Element of [: the carrier of R, the carrier of R:]
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( b1 = {} or ( not b1 = {} & not b2 = {} & not (R,b1) = (R,b2) & [(R,b1),(R,b2)] in the InternalRel of R ) ) } is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in a2 ) } is set
A is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in A ) } is set
FCR is Relation-like Function-like set
dom FCR is set
FCR . 0 is set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
FCR . A is set
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FCR . (A + 1) is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in FCR . A ) } is set
A is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z is set
aStart is finite Element of Fin the carrier of R
SS is finite Element of Fin the carrier of R
[aStart,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,SS} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,SS},{aStart}} is non empty finite V34() set
(R,aStart) is Element of the carrier of R
(R,SS) is Element of the carrier of R
[(R,aStart),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,aStart),(R,SS)} is non empty finite set
{(R,aStart)} is non empty trivial finite 1 -element set
{{(R,aStart),(R,SS)},{(R,aStart)}} is non empty finite V34() set
FCR . A is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz - 1 is V42() V43() ext-real Element of REAL
(zz - 1) + 1 is V42() V43() ext-real Element of REAL
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
FCR . zz is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in FCR . zz ) } is set
FCR . zz is set
aStart is set
SS is finite Element of Fin the carrier of R
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,SS) is Element of the carrier of R
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
SS \ {(R,SS)} is finite Element of bool SS
[(SS \ {(R,SS)}),(SS \ {(R,SS)})] is V1() Element of [:(bool SS),(bool SS):]
[:(bool SS),(bool SS):] is non empty Relation-like finite set
{(SS \ {(R,SS)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(SS \ {(R,SS)})} is non empty trivial finite V34() 1 -element set
{{(SS \ {(R,SS)}),(SS \ {(R,SS)})},{(SS \ {(R,SS)})}} is non empty finite V34() set
FCR . A is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
A is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
dom A is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
A . 0 is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A . (zz + 1) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
A . zz is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in A . zz ) } is set
FCR is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
dom FCR is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
FCR . 0 is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
A is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
dom A is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
A . 0 is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in a2 ) } is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
FCR . (zz + 1) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
FCR . zz is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in FCR . zz ) } is set
zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
A . (zz + 1) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
A . zz is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in A . zz ) } is set
Z is set
zz is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in zz ) } is set
aStart is set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is finite Element of Fin the carrier of R
CR is finite Element of Fin the carrier of R
[IR,CR] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{IR,CR} is non empty finite V34() set
{IR} is non empty trivial finite V34() 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
(R,IR) is Element of the carrier of R
(R,CR) is Element of the carrier of R
[(R,IR),(R,CR)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,IR),(R,CR)} is non empty finite set
{(R,IR)} is non empty trivial finite 1 -element set
{{(R,IR),(R,CR)},{(R,IR)}} is non empty finite V34() set
bool IR is non empty finite V34() cup-closed diff-closed preBoolean set
bool CR is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,IR)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
IR \ {(R,IR)} is finite Element of bool IR
{(R,CR)} is non empty trivial finite 1 -element Element of bool the carrier of R
CR \ {(R,CR)} is finite Element of bool CR
[(IR \ {(R,IR)}),(CR \ {(R,CR)})] is V1() Element of [:(bool IR),(bool CR):]
[:(bool IR),(bool CR):] is non empty Relation-like finite set
{(IR \ {(R,IR)}),(CR \ {(R,CR)})} is non empty finite V34() set
{(IR \ {(R,IR)})} is non empty trivial finite V34() 1 -element set
{{(IR \ {(R,IR)}),(CR \ {(R,CR)})},{(IR \ {(R,IR)})}} is non empty finite V34() set
(R) . 0 is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( b1 = {} or ( not b1 = {} & not b2 = {} & not (R,b1) = (R,b2) & [(R,b1),(R,b2)] in the InternalRel of R ) ) } is set
dom (R) is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
zz is set
zz is set
(R) . zz is set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
aStart is finite Element of Fin the carrier of R
SS is finite Element of Fin the carrier of R
[aStart,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,SS} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,SS},{aStart}} is non empty finite V34() set
(R,aStart) is Element of the carrier of R
(R,SS) is Element of the carrier of R
[(R,aStart),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,aStart),(R,SS)} is non empty finite set
{(R,aStart)} is non empty trivial finite 1 -element set
{{(R,aStart),(R,SS)},{(R,aStart)}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Z - 1 is V42() V43() ext-real Element of REAL
(Z - 1) + 1 is V42() V43() ext-real Element of REAL
(R) . ((Z - 1) + 1) is set
(R) . (Z - 1) is set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in (R) . (Z - 1) ) } is set
aStart is finite Element of Fin the carrier of R
SS is finite Element of Fin the carrier of R
[aStart,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,SS} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,SS},{aStart}} is non empty finite V34() set
(R,aStart) is Element of the carrier of R
(R,SS) is Element of the carrier of R
bool aStart is non empty finite V34() cup-closed diff-closed preBoolean set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,aStart)} is non empty trivial finite 1 -element Element of bool the carrier of R
aStart \ {(R,aStart)} is finite Element of bool aStart
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
SS \ {(R,SS)} is finite Element of bool SS
[(aStart \ {(R,aStart)}),(SS \ {(R,SS)})] is V1() Element of [:(bool aStart),(bool SS):]
[:(bool aStart),(bool SS):] is non empty Relation-like finite set
{(aStart \ {(R,aStart)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(aStart \ {(R,aStart)})} is non empty trivial finite V34() 1 -element set
{{(aStart \ {(R,aStart)}),(SS \ {(R,SS)})},{(aStart \ {(R,aStart)})}} is non empty finite V34() set
Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
zz is set
Z is set
(R) . Z is set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
aStart + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(R) . (aStart + 1) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
(R) . aStart is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( not b1 = {} & not b2 = {} & (R,b1) = (R,b2) & [(b1 \ {(R,b1)}),(b2 \ {(R,b2)})] in (R) . aStart ) } is set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
IR is finite Element of Fin the carrier of R
[IR,{}] is V1() set
{IR,{}} is non empty finite V34() set
{IR} is non empty trivial finite V34() 1 -element set
{{IR,{}},{IR}} is non empty finite V34() set
FCR is finite Element of Fin the carrier of R
[IR,FCR] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{IR,FCR} is non empty finite V34() set
{{IR,FCR},{IR}} is non empty finite V34() set
(R,IR) is Element of the carrier of R
(R,FCR) is Element of the carrier of R
[(R,IR),(R,FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{(R,IR),(R,FCR)} is non empty finite set
{(R,IR)} is non empty trivial finite 1 -element set
{{(R,IR),(R,FCR)},{(R,IR)}} is non empty finite V34() set
(R,IR) is Element of the carrier of R
(R,FCR) is Element of the carrier of R
bool IR is non empty finite V34() cup-closed diff-closed preBoolean set
bool {} is non empty finite V34() cup-closed diff-closed preBoolean set
IR \ (R,IR) is finite Element of bool IR
{} \ (R,FCR) is empty non proper Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() Element of bool {}
[(IR \ (R,IR)),({} \ (R,FCR))] is V1() Element of [:(bool IR),(bool {}):]
[:(bool IR),(bool {}):] is non empty Relation-like finite set
{(IR \ (R,IR)),({} \ (R,FCR))} is non empty finite V34() set
{(IR \ (R,IR))} is non empty trivial finite V34() 1 -element set
{{(IR \ (R,IR)),({} \ (R,FCR))},{(IR \ (R,IR))}} is non empty finite V34() set
(R,IR) is Element of the carrier of R
(R,FCR) is Element of the carrier of R
[(R,IR),(R,FCR)] is V1() Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{(R,IR),(R,FCR)} is non empty finite set
{(R,IR)} is non empty trivial finite 1 -element set
{{(R,IR),(R,FCR)},{(R,IR)}} is non empty finite V34() set
bool IR is non empty finite V34() cup-closed diff-closed preBoolean set
bool {} is non empty finite V34() cup-closed diff-closed preBoolean set
IR \ (R,IR) is finite Element of bool IR
{} \ (R,FCR) is empty non proper Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V34() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V42() V43() ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V72() V73() V74() V75() V76() V77() V78() FinSequence-yielding finite-support V295() V296() V297() V298() Element of bool {}
[(IR \ (R,IR)),({} \ (R,FCR))] is V1() Element of [:(bool IR),(bool {}):]
[:(bool IR),(bool {}):] is non empty Relation-like finite set
{(IR \ (R,IR)),({} \ (R,FCR))} is non empty finite V34() set
{(IR \ (R,IR))} is non empty trivial finite V34() 1 -element set
{{(IR \ (R,IR)),({} \ (R,FCR))},{(IR \ (R,IR))}} is non empty finite V34() set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
IR is finite Element of Fin the carrier of R
(R,IR) is Element of the carrier of R
{(R,IR)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
IR \ {(R,IR)} is finite Element of bool IR
bool IR is non empty finite V34() cup-closed diff-closed preBoolean set
FIR is finite set
FIR \ {(R,IR)} is finite Element of bool FIR
bool FIR is non empty finite V34() cup-closed diff-closed preBoolean set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
IR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
CR is finite Element of Fin the carrier of R
card CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
(R,CR) is Element of the carrier of R
{(R,CR)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
CR \ {(R,CR)} is finite Element of bool CR
bool CR is non empty finite V34() cup-closed diff-closed preBoolean set
card (CR \ {(R,CR)}) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
FCR is set
FIR is finite set
FIR \ {(R,CR)} is finite Element of bool FIR
bool FIR is non empty finite V34() cup-closed diff-closed preBoolean set
card (FIR \ {(R,CR)}) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
card FIR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
card {(R,CR)} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of omega
(card FIR) - (card {(R,CR)}) is V42() V43() ext-real set
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
{ [b1,b2] where b1, b2 is finite Element of Fin the carrier of R : ( b1 = {} or ( not b1 = {} & not b2 = {} & not (R,b1) = (R,b2) & [(R,b1),(R,b2)] in the InternalRel of R ) ) } is set
(R) . 0 is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
zz is set
zz is set
zz is set
dom (R) is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
aStart is finite Element of Fin the carrier of R
card aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
[aStart,aStart] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,aStart} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,aStart},{aStart}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
aStart + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
S01 is finite Element of Fin the carrier of R
card S01 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
[S01,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S01,S01} is non empty finite V34() set
{S01} is non empty trivial finite V34() 1 -element set
{{S01,S01},{S01}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Z is finite Element of Fin the carrier of R
card Z is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
[zz,zz] is V1() set
{zz,zz} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,zz},{zz}} is non empty finite V34() set
zz is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
zz is set
Z is set
[zz,Z] is V1() set
{zz,Z} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
[Z,zz] is V1() set
{Z,zz} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,zz},{Z}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
S01 is finite set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
[S01,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S01,SS} is non empty finite V34() set
{S01} is non empty trivial finite V34() 1 -element set
{{S01,SS},{S01}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
[(R,SS),(R,S01)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,S01)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,S01)},{(R,SS)}} is non empty finite V34() set
[(R,S01),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,SS)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,SS)},{(R,S01)}} is non empty finite V34() set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
S01 \ {(R,S01)} is finite Element of bool S01
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
SS \ {(R,SS)} is finite Element of bool SS
[(S01 \ {(R,S01)}),(SS \ {(R,SS)})] is V1() Element of [:(bool S01),(bool SS):]
[:(bool S01),(bool SS):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(SS \ {(R,SS)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
[(R,S01),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,SS)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,SS)},{(R,S01)}} is non empty finite V34() set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
S01 \ {(R,S01)} is finite Element of bool S01
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
SS \ {(R,SS)} is finite Element of bool SS
[(S01 \ {(R,S01)}),(SS \ {(R,SS)})] is V1() Element of [:(bool S01),(bool SS):]
[:(bool S01),(bool SS):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(SS \ {(R,SS)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
S01 \ {(R,S01)} is finite Element of bool S01
[(SS \ {(R,SS)}),(S01 \ {(R,S01)})] is V1() Element of [:(bool SS),(bool S01):]
[:(bool SS),(bool S01):] is non empty Relation-like finite set
{(SS \ {(R,SS)}),(S01 \ {(R,S01)})} is non empty finite V34() set
{(SS \ {(R,SS)})} is non empty trivial finite V34() 1 -element set
{{(SS \ {(R,SS)}),(S01 \ {(R,S01)})},{(SS \ {(R,SS)})}} is non empty finite V34() set
[(R,S01),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,SS)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,SS)},{(R,S01)}} is non empty finite V34() set
[(S01 \ {(R,S01)}),(SS \ {(R,SS)})] is V1() Element of [:(bool S01),(bool SS):]
[:(bool S01),(bool SS):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(SS \ {(R,SS)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
S02 is finite set
S02 \ {(R,SS)} is finite Element of bool S02
bool S02 is non empty finite V34() cup-closed diff-closed preBoolean set
S0max is finite set
S0max \ {(R,S01)} is finite Element of bool S0max
bool S0max is non empty finite V34() cup-closed diff-closed preBoolean set
b0t is finite Element of Fin the carrier of R
card b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
b0 is finite Element of Fin the carrier of R
S is set
{(R,SS)} \/ b0t is non empty finite set
S is set
[(R,S01),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,SS)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,SS)},{(R,S01)}} is non empty finite V34() set
[(S01 \ {(R,S01)}),(SS \ {(R,SS)})] is V1() Element of [:(bool S01),(bool SS):]
[:(bool S01),(bool SS):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(SS \ {(R,SS)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(SS \ {(R,SS)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
[(R,SS),(R,S01)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,S01)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,S01)},{(R,SS)}} is non empty finite V34() set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
S01 \ {(R,S01)} is finite Element of bool S01
[(SS \ {(R,SS)}),(S01 \ {(R,S01)})] is V1() Element of [:(bool SS),(bool S01):]
[:(bool SS),(bool S01):] is non empty Relation-like finite set
{(SS \ {(R,SS)}),(S01 \ {(R,S01)})} is non empty finite V34() set
{(SS \ {(R,SS)})} is non empty trivial finite V34() 1 -element set
{{(SS \ {(R,SS)}),(S01 \ {(R,S01)})},{(SS \ {(R,SS)})}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
[S01,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S01,SS} is non empty finite V34() set
{S01} is non empty trivial finite V34() 1 -element set
{{S01,SS},{S01}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
aStart is finite Element of Fin the carrier of R
card aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
zz is set
Z is set
aStart is set
[zz,Z] is V1() set
{zz,Z} is non empty finite set
{zz} is non empty trivial finite 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
[Z,aStart] is V1() set
{Z,aStart} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,aStart},{Z}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
S02 is finite set
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{{SS,S01},{SS}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{{SS,S01},{SS}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
S02 is finite Element of Fin the carrier of R
[S01,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S01,S02} is non empty finite V34() set
{S01} is non empty trivial finite V34() 1 -element set
{{S01,S02},{S01}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
[(R,SS),(R,S01)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,S01)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,S01)},{(R,SS)}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
[(R,S01),(R,S02)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,S02)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,S02)},{(R,S01)}} is non empty finite V34() set
[(R,SS),(R,S02)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,S02)} is non empty finite set
{{(R,SS),(R,S02)},{(R,SS)}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
bool S02 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
S01 \ {(R,S01)} is finite Element of bool S01
{(R,S02)} is non empty trivial finite 1 -element Element of bool the carrier of R
S02 \ {(R,S02)} is finite Element of bool S02
[(S01 \ {(R,S01)}),(S02 \ {(R,S02)})] is V1() Element of [:(bool S01),(bool S02):]
[:(bool S01),(bool S02):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
[(R,S01),(R,S02)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,S02)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,S02)},{(R,S01)}} is non empty finite V34() set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
bool S02 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
S01 \ {(R,S01)} is finite Element of bool S01
{(R,S02)} is non empty trivial finite 1 -element Element of bool the carrier of R
S02 \ {(R,S02)} is finite Element of bool S02
[(S01 \ {(R,S01)}),(S02 \ {(R,S02)})] is V1() Element of [:(bool S01),(bool S02):]
[:(bool S01),(bool S02):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
S01 \ {(R,S01)} is finite Element of bool S01
[(SS \ {(R,SS)}),(S01 \ {(R,S01)})] is V1() Element of [:(bool SS),(bool S01):]
[:(bool SS),(bool S01):] is non empty Relation-like finite set
{(SS \ {(R,SS)}),(S01 \ {(R,S01)})} is non empty finite V34() set
{(SS \ {(R,SS)})} is non empty trivial finite V34() 1 -element set
{{(SS \ {(R,SS)}),(S01 \ {(R,S01)})},{(SS \ {(R,SS)})}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
[(R,S01),(R,S02)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,S02)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,S02)},{(R,S01)}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
bool S02 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S02)} is non empty trivial finite 1 -element Element of bool the carrier of R
S02 \ {(R,S02)} is finite Element of bool S02
[(S01 \ {(R,S01)}),(S02 \ {(R,S02)})] is V1() Element of [:(bool S01),(bool S02):]
[:(bool S01),(bool S02):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
a0 is finite Element of Fin the carrier of R
card a0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
i0 is finite set
i0 \ {(R,S02)} is finite Element of bool i0
bool i0 is non empty finite V34() cup-closed diff-closed preBoolean set
S is finite set
S \ {(R,S01)} is finite Element of bool S
bool S is non empty finite V34() cup-closed diff-closed preBoolean set
a is finite Element of Fin the carrier of R
[a0,a] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{a0,a} is non empty finite V34() set
{a0} is non empty trivial finite V34() 1 -element set
{{a0,a},{a0}} is non empty finite V34() set
b0 is finite Element of Fin the carrier of R
[a0,b0] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{a0,b0} is non empty finite V34() set
{{a0,b0},{a0}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,S02) is Element of the carrier of R
[(R,S01),(R,S02)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,S01),(R,S02)} is non empty finite set
{(R,S01)} is non empty trivial finite 1 -element set
{{(R,S01),(R,S02)},{(R,S01)}} is non empty finite V34() set
bool S02 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,S02)} is non empty trivial finite 1 -element Element of bool the carrier of R
S02 \ {(R,S02)} is finite Element of bool S02
[(S01 \ {(R,S01)}),(S02 \ {(R,S02)})] is V1() Element of [:(bool S01),(bool S02):]
[:(bool S01),(bool S02):] is non empty Relation-like finite set
{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})} is non empty finite V34() set
{(S01 \ {(R,S01)})} is non empty trivial finite V34() 1 -element set
{{(S01 \ {(R,S01)}),(S02 \ {(R,S02)})},{(S01 \ {(R,S01)})}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,S01) is Element of the carrier of R
[(R,SS),(R,S01)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,S01)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,S01)},{(R,SS)}} is non empty finite V34() set
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
bool S01 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
{(R,S01)} is non empty trivial finite 1 -element Element of bool the carrier of R
S01 \ {(R,S01)} is finite Element of bool S01
[(SS \ {(R,SS)}),(S01 \ {(R,S01)})] is V1() Element of [:(bool SS),(bool S01):]
[:(bool SS),(bool S01):] is non empty Relation-like finite set
{(SS \ {(R,SS)}),(S01 \ {(R,S01)})} is non empty finite V34() set
{(SS \ {(R,SS)})} is non empty trivial finite V34() 1 -element set
{{(SS \ {(R,SS)}),(S01 \ {(R,S01)})},{(SS \ {(R,SS)})}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 is finite Element of Fin the carrier of R
[SS,S01] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S01} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,S01},{SS}} is non empty finite V34() set
S02 is finite Element of Fin the carrier of R
[S01,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S01,S02} is non empty finite V34() set
{S01} is non empty trivial finite V34() 1 -element set
{{S01,S02},{S01}} is non empty finite V34() set
[SS,S02] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,S02} is non empty finite V34() set
{{SS,S02},{SS}} is non empty finite V34() set
SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
[zz,aStart] is V1() set
{zz,aStart} is non empty finite set
{{zz,aStart},{zz}} is non empty finite V34() set
zz is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
dom zz is Element of bool (Fin the carrier of R)
bool (Fin the carrier of R) is non empty cup-closed diff-closed preBoolean set
field zz is set
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
R is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued total V18( Fin the carrier of R, Fin the carrier of R) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
RelStr(# (Fin the carrier of R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is total reflexive transitive antisymmetric RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued total V18( Fin the carrier of R, Fin the carrier of R) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
RelStr(# (Fin the carrier of R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is non empty total reflexive transitive antisymmetric RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued total V18( Fin the carrier of R, Fin the carrier of R) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
RelStr(# (Fin the carrier of R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the carrier of (R) is non empty set
the InternalRel of (R) is Relation-like the carrier of (R) -defined the carrier of (R) -valued total V18( the carrier of (R), the carrier of (R)) reflexive antisymmetric transitive Element of bool [: the carrier of (R), the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is non empty Relation-like set
bool [: the carrier of (R), the carrier of (R):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
IR is Element of the carrier of (R)
CR is Element of the carrier of (R)
[IR,CR] is V1() Element of [: the carrier of (R), the carrier of (R):]
{IR,CR} is non empty finite set
{IR} is non empty trivial finite 1 -element set
{{IR,CR},{IR}} is non empty finite V34() set
FCR is finite Element of Fin the carrier of R
A is finite Element of Fin the carrier of R
zz is finite Element of Fin the carrier of R
zz is finite Element of Fin the carrier of R
(R,zz) is Element of the carrier of R
(R,zz) is Element of the carrier of R
[(R,zz),(R,zz)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,zz),(R,zz)} is non empty finite set
{(R,zz)} is non empty trivial finite 1 -element set
{{(R,zz),(R,zz)},{(R,zz)}} is non empty finite V34() set
bool zz is non empty finite V34() cup-closed diff-closed preBoolean set
bool zz is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,zz)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
zz \ {(R,zz)} is finite Element of bool zz
{(R,zz)} is non empty trivial finite 1 -element Element of bool the carrier of R
zz \ {(R,zz)} is finite Element of bool zz
[(zz \ {(R,zz)}),(zz \ {(R,zz)})] is V1() Element of [:(bool zz),(bool zz):]
[:(bool zz),(bool zz):] is non empty Relation-like finite set
{(zz \ {(R,zz)}),(zz \ {(R,zz)})} is non empty finite V34() set
{(zz \ {(R,zz)})} is non empty trivial finite V34() 1 -element set
{{(zz \ {(R,zz)}),(zz \ {(R,zz)})},{(zz \ {(R,zz)})}} is non empty finite V34() set
zz is finite Element of Fin the carrier of R
zz is finite Element of Fin the carrier of R
(R,zz) is Element of the carrier of R
(R,zz) is Element of the carrier of R
[(R,zz),(R,zz)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,zz),(R,zz)} is non empty finite set
{(R,zz)} is non empty trivial finite 1 -element set
{{(R,zz),(R,zz)},{(R,zz)}} is non empty finite V34() set
bool zz is non empty finite V34() cup-closed diff-closed preBoolean set
bool zz is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,zz)} is non empty trivial finite 1 -element Element of bool the carrier of R
zz \ {(R,zz)} is finite Element of bool zz
{(R,zz)} is non empty trivial finite 1 -element Element of bool the carrier of R
zz \ {(R,zz)} is finite Element of bool zz
[(zz \ {(R,zz)}),(zz \ {(R,zz)})] is V1() Element of [:(bool zz),(bool zz):]
[:(bool zz),(bool zz):] is non empty Relation-like finite set
{(zz \ {(R,zz)}),(zz \ {(R,zz)})} is non empty finite V34() set
{(zz \ {(R,zz)})} is non empty trivial finite V34() 1 -element set
{{(zz \ {(R,zz)}),(zz \ {(R,zz)})},{(zz \ {(R,zz)})}} is non empty finite V34() set
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is non empty total reflexive transitive antisymmetric RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued total V18( Fin the carrier of R, Fin the carrier of R) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
RelStr(# (Fin the carrier of R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
the carrier of (R) is non empty set
A is Element of the carrier of (R)
zz is Element of the carrier of (R)
aStart is finite Element of Fin the carrier of R
card aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[aStart,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,SS} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,SS},{aStart}} is non empty finite V34() set
aStart is finite Element of Fin the carrier of R
card aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
SS is finite Element of Fin the carrier of R
[aStart,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{aStart,SS} is non empty finite V34() set
{aStart} is non empty trivial finite V34() 1 -element set
{{aStart,SS},{aStart}} is non empty finite V34() set
[SS,aStart] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,aStart} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,aStart},{SS}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
aStart + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
(R,SS) is Element of the carrier of R
(R,SS) is Element of the carrier of R
[(R,SS),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,SS)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,SS)},{(R,SS)}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[(R,SS),(R,SS)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,SS),(R,SS)} is non empty finite set
{(R,SS)} is non empty trivial finite 1 -element set
{{(R,SS),(R,SS)},{(R,SS)}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,SS) is Element of the carrier of R
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
SS \ {(R,SS)} is finite Element of bool SS
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,SS)} is non empty trivial finite 1 -element Element of bool the carrier of R
SS \ {(R,SS)} is finite Element of bool SS
bool SS is non empty finite V34() cup-closed diff-closed preBoolean set
card (SS \ {(R,SS)}) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
S0max is finite Element of Fin the carrier of R
a0 is finite Element of Fin the carrier of R
[S0max,a0] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S0max,a0} is non empty finite V34() set
{S0max} is non empty trivial finite V34() 1 -element set
{{S0max,a0},{S0max}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
a0 is finite Element of Fin the carrier of R
S0max is finite Element of Fin the carrier of R
[a0,S0max] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{a0,S0max} is non empty finite V34() set
{a0} is non empty trivial finite V34() 1 -element set
{{a0,S0max},{a0}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
S0max is finite Element of Fin the carrier of R
a0 is finite Element of Fin the carrier of R
[S0max,a0] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{S0max,a0} is non empty finite V34() set
{S0max} is non empty trivial finite V34() 1 -element set
{{S0max,a0},{S0max}} is non empty finite V34() set
[a0,S0max] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{a0,S0max} is non empty finite V34() set
{a0} is non empty trivial finite V34() 1 -element set
{{a0,S0max},{a0}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
(R,SS) is Element of the carrier of R
(R,SS) is Element of the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
SS is finite Element of Fin the carrier of R
card SS is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
aStart + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
SS is finite Element of Fin the carrier of R
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
[SS,SS] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{SS,SS} is non empty finite V34() set
{SS} is non empty trivial finite V34() 1 -element set
{{SS,SS},{SS}} is non empty finite V34() set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
zz is finite Element of Fin the carrier of R
card zz is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of omega
Z is finite Element of Fin the carrier of R
[zz,Z] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{zz,Z} is non empty finite V34() set
{zz} is non empty trivial finite V34() 1 -element set
{{zz,Z},{zz}} is non empty finite V34() set
[Z,zz] is V1() Element of [:(Fin the carrier of R),(Fin the carrier of R):]
{Z,zz} is non empty finite V34() set
{Z} is non empty trivial finite V34() 1 -element set
{{Z,zz},{Z}} is non empty finite V34() set
R is non empty connected RelStr
IR is non empty set
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
FCR is set
the InternalRel of R -Seg FCR is set
A is Element of the carrier of R
CR is Element of the carrier of R
FIR is Element of the carrier of R
[CR,FIR] is V1() Element of [: the carrier of R, the carrier of R:]
{CR,FIR} is non empty finite set
{CR} is non empty trivial finite 1 -element set
{{CR,FIR},{CR}} is non empty finite V34() set
the InternalRel of R -Seg FIR is set
( the InternalRel of R -Seg FIR) /\ IR is set
[FIR,CR] is V1() Element of [: the carrier of R, the carrier of R:]
{FIR,CR} is non empty finite set
{FIR} is non empty trivial finite 1 -element set
{{FIR,CR},{FIR}} is non empty finite V34() set
the InternalRel of R -Seg CR is set
( the InternalRel of R -Seg CR) /\ IR is set
R is non empty RelStr
the carrier of R is non empty set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
IR is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
IR ^\ CR is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
A + CR is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(IR ^\ CR) . A is Element of the carrier of R
IR . (A + CR) is Element of the carrier of R
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(IR ^\ CR) . (A + 1) is Element of the carrier of R
(A + 1) + CR is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
IR . ((A + 1) + CR) is Element of the carrier of R
(A + CR) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
IR . ((A + CR) + 1) is Element of the carrier of R
[((IR ^\ CR) . (A + 1)),((IR ^\ CR) . A)] is V1() Element of [: the carrier of R, the carrier of R:]
{((IR ^\ CR) . (A + 1)),((IR ^\ CR) . A)} is non empty finite set
{((IR ^\ CR) . (A + 1))} is non empty trivial finite 1 -element set
{{((IR ^\ CR) . (A + 1)),((IR ^\ CR) . A)},{((IR ^\ CR) . (A + 1))}} is non empty finite V34() set
R is non empty total reflexive transitive antisymmetric connected RelStr
(R) is non empty total reflexive transitive antisymmetric connected RelStr
the carrier of R is non empty set
Fin the carrier of R is non empty cup-closed diff-closed preBoolean set
(R) is Relation-like Fin the carrier of R -defined Fin the carrier of R -valued total V18( Fin the carrier of R, Fin the carrier of R) reflexive antisymmetric transitive Element of bool [:(Fin the carrier of R),(Fin the carrier of R):]
[:(Fin the carrier of R),(Fin the carrier of R):] is non empty Relation-like set
bool [:(Fin the carrier of R),(Fin the carrier of R):] is non empty cup-closed diff-closed preBoolean set
(R) is non empty Relation-like NAT -defined bool [:(Fin the carrier of R),(Fin the carrier of R):] -valued Function-like total V18( NAT , bool [:(Fin the carrier of R),(Fin the carrier of R):]) Element of bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):]
[:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bool [:(Fin the carrier of R),(Fin the carrier of R):]):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
rng (R) is non empty set
union (rng (R)) is set
RelStr(# (Fin the carrier of R),(R) #) is non empty strict total reflexive transitive antisymmetric RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued total V18( the carrier of R, the carrier of R) reflexive antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty cup-closed diff-closed preBoolean set
the carrier of (R) is non empty set
[:NAT, the carrier of (R):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (R):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
A is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{ b1 where b1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):] : b1 is descending } is set
zz is non empty set
[: the carrier of R,zz:] is non empty Relation-like set
[:NAT, the carrier of R:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of R:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
aStart is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
SS is Element of [: the carrier of R,zz:]
SS `2 is set
SS `2 is Element of zz
S02 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S01 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S01 . S02 is Element of the carrier of (R)
S02 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 . (S02 + 1) is Element of the carrier of (R)
S0max is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
[(S01 . (S02 + 1)),(S01 . S02)] is V1() Element of [: the carrier of (R), the carrier of (R):]
[: the carrier of (R), the carrier of (R):] is non empty Relation-like set
{(S01 . (S02 + 1)),(S01 . S02)} is non empty finite set
{(S01 . (S02 + 1))} is non empty trivial finite 1 -element set
{{(S01 . (S02 + 1)),(S01 . S02)},{(S01 . (S02 + 1))}} is non empty finite V34() set
S0max is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S02 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . S02 is Element of the carrier of (R)
a0 is finite Element of Fin the carrier of R
(R,a0) is Element of the carrier of R
S02 is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
rng S02 is non empty set
(R,(rng S02)) is Element of the carrier of R
S02 mindex (R,(rng S02)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 ^\ (S02 mindex (R,(rng S02))) is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{(R,(rng S02))} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S01 ^\ (S02 mindex (R,(rng S02)))) . b0t is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t) is non empty cup-closed diff-closed preBoolean set
S is finite Element of bool the carrier of R
S \ {(R,(rng S02))} is finite Element of bool the carrier of R
a is finite Element of Fin the carrier of R
b is finite Element of Fin the carrier of R
n is finite Element of Fin the carrier of R
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(S01 ^\ (S02 mindex (R,(rng S02)))) . b0t is set
((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . b0t) is non empty cup-closed diff-closed preBoolean set
dom S02 is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
(S02 mindex (R,(rng S02))) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 . ((S02 mindex (R,(rng S02))) + 0) is Element of the carrier of R
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S02 mindex (R,(rng S02))) + b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 . ((S02 mindex (R,(rng S02))) + b0t) is Element of the carrier of R
b0t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(S02 mindex (R,(rng S02))) + (b0t + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
((S02 mindex (R,(rng S02))) + b0t) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S01 . ((S02 mindex (R,(rng S02))) + b0t) is Element of the carrier of (R)
a is finite Element of Fin the carrier of R
(R,a) is Element of the carrier of R
S01 . ((S02 mindex (R,(rng S02))) + (b0t + 1)) is Element of the carrier of (R)
S02 . ((S02 mindex (R,(rng S02))) + (b0t + 1)) is Element of the carrier of R
n is finite Element of Fin the carrier of R
(R,n) is Element of the carrier of R
i is Element of the carrier of (R)
b is Element of the carrier of (R)
[i,b] is V1() Element of [: the carrier of (R), the carrier of (R):]
{i,b} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,b},{i}} is non empty finite V34() set
n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
n1 is finite Element of Fin the carrier of R
n1 is finite Element of Fin the carrier of R
(R,n1) is Element of the carrier of R
(R,n1) is Element of the carrier of R
[(R,n1),(R,n1)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,n1),(R,n1)} is non empty finite set
{(R,n1)} is non empty trivial finite 1 -element set
{{(R,n1),(R,n1)},{(R,n1)}} is non empty finite V34() set
bool n1 is non empty finite V34() cup-closed diff-closed preBoolean set
bool n1 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,n1)} is non empty trivial finite 1 -element Element of bool the carrier of R
n1 \ {(R,n1)} is finite Element of bool n1
{(R,n1)} is non empty trivial finite 1 -element Element of bool the carrier of R
n1 \ {(R,n1)} is finite Element of bool n1
[(n1 \ {(R,n1)}),(n1 \ {(R,n1)})] is V1() Element of [:(bool n1),(bool n1):]
[:(bool n1),(bool n1):] is non empty Relation-like finite set
{(n1 \ {(R,n1)}),(n1 \ {(R,n1)})} is non empty finite V34() set
{(n1 \ {(R,n1)})} is non empty trivial finite V34() 1 -element set
{{(n1 \ {(R,n1)}),(n1 \ {(R,n1)})},{(n1 \ {(R,n1)})}} is non empty finite V34() set
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S02 mindex (R,(rng S02))) + b0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S02 mindex (R,(rng S02))) + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 . b0t is Element of the carrier of R
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S01 . b0t is Element of the carrier of (R)
b0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 . b0 is Element of the carrier of R
S is finite Element of Fin the carrier of R
(R,S) is Element of the carrier of R
a is finite Element of Fin the carrier of R
(R,a) is Element of the carrier of R
b0t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S01 ^\ (S02 mindex (R,(rng S02)))) . b0t is Element of the carrier of (R)
S is finite Element of Fin the carrier of R
a is finite Element of Fin the carrier of R
b0t + (S02 mindex (R,(rng S02))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . (b0t + (S02 mindex (R,(rng S02)))) is Element of the carrier of (R)
(R,a) is Element of the carrier of R
n is finite Element of Fin the carrier of R
(R,n) is Element of the carrier of R
[:NAT,(Fin the carrier of R):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Fin the carrier of R):] is non empty non trivial non finite cup-closed diff-closed preBoolean set
b0t is non empty Relation-like NAT -defined Fin the carrier of R -valued Function-like total V18( NAT , Fin the carrier of R) Element of bool [:NAT,(Fin the carrier of R):]
b0 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
[(R,(rng S02)),b0] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
[: the carrier of R,(bool [:NAT, the carrier of (R):]):] is non empty non trivial Relation-like non finite set
{(R,(rng S02)),b0} is non empty finite set
{(R,(rng S02))} is non empty trivial finite 1 -element set
{{(R,(rng S02)),b0},{(R,(rng S02))}} is non empty finite V34() set
a is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(S01 ^\ (S02 mindex (R,(rng S02)))) . a is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . a) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a) is non empty cup-closed diff-closed preBoolean set
b0 . a is Element of the carrier of (R)
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
(S01 ^\ (S02 mindex (R,(rng S02)))) . (a + 1) is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . (a + 1)) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . (a + 1))
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . (a + 1)) is non empty cup-closed diff-closed preBoolean set
b0 . (a + 1) is Element of the carrier of (R)
(S01 ^\ (S02 mindex (R,(rng S02)))) . a is Element of the carrier of (R)
n is Element of the carrier of (R)
b is Element of the carrier of (R)
[b,n] is V1() Element of [: the carrier of (R), the carrier of (R):]
{b,n} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,n},{b}} is non empty finite V34() set
n1 is finite Element of Fin the carrier of R
Sn12 is finite Element of Fin the carrier of R
(R,n1) is Element of the carrier of R
(R,Sn12) is Element of the carrier of R
[(R,n1),(R,Sn12)] is V1() Element of [: the carrier of R, the carrier of R:]
{(R,n1),(R,Sn12)} is non empty finite set
{(R,n1)} is non empty trivial finite 1 -element set
{{(R,n1),(R,Sn12)},{(R,n1)}} is non empty finite V34() set
bool n1 is non empty finite V34() cup-closed diff-closed preBoolean set
bool Sn12 is non empty finite V34() cup-closed diff-closed preBoolean set
{(R,n1)} is non empty trivial finite 1 -element Element of bool the carrier of R
n1 \ {(R,n1)} is finite Element of bool n1
{(R,Sn12)} is non empty trivial finite 1 -element Element of bool the carrier of R
Sn12 \ {(R,Sn12)} is finite Element of bool Sn12
[(n1 \ {(R,n1)}),(Sn12 \ {(R,Sn12)})] is V1() Element of [:(bool n1),(bool Sn12):]
[:(bool n1),(bool Sn12):] is non empty Relation-like finite set
{(n1 \ {(R,n1)}),(Sn12 \ {(R,Sn12)})} is non empty finite V34() set
{(n1 \ {(R,n1)})} is non empty trivial finite V34() 1 -element set
{{(n1 \ {(R,n1)}),(Sn12 \ {(R,Sn12)})},{(n1 \ {(R,n1)})}} is non empty finite V34() set
Sn1max is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
(S01 ^\ (S02 mindex (R,(rng S02)))) . Sn1max is Element of the carrier of (R)
Sn1max + (S02 mindex (R,(rng S02))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S01 . (Sn1max + (S02 mindex (R,(rng S02)))) is Element of the carrier of (R)
i is finite Element of Fin the carrier of R
(R,i) is Element of the carrier of R
n1 is finite Element of Fin the carrier of R
(R,n1) is Element of the carrier of R
Sn1max is finite Element of Fin the carrier of R
(R,Sn1max) is Element of the carrier of R
an1 is finite Element of Fin the carrier of R
(R,an1) is Element of the carrier of R
b0 . a is Element of the carrier of (R)
Sn1max is finite Element of Fin the carrier of R
an1 is finite Element of Fin the carrier of R
[(b0 . (a + 1)),(b0 . a)] is V1() Element of [: the carrier of (R), the carrier of (R):]
{(b0 . (a + 1)),(b0 . a)} is non empty finite set
{(b0 . (a + 1))} is non empty trivial finite 1 -element set
{{(b0 . (a + 1)),(b0 . a)},{(b0 . (a + 1))}} is non empty finite V34() set
[(b0 . (a + 1)),(b0 . a)] is V1() Element of [: the carrier of (R), the carrier of (R):]
{(b0 . (a + 1)),(b0 . a)} is non empty finite set
{(b0 . (a + 1))} is non empty trivial finite 1 -element set
{{(b0 . (a + 1)),(b0 . a)},{(b0 . (a + 1))}} is non empty finite V34() set
[(b0 . (a + 1)),(b0 . a)] is V1() Element of [: the carrier of (R), the carrier of (R):]
{(b0 . (a + 1)),(b0 . a)} is non empty finite set
{(b0 . (a + 1))} is non empty trivial finite 1 -element set
{{(b0 . (a + 1)),(b0 . a)},{(b0 . (a + 1))}} is non empty finite V34() set
Sn1max is finite Element of Fin the carrier of R
an1 is finite Element of Fin the carrier of R
a is Element of [: the carrier of R,zz:]
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S01 . a is Element of the carrier of (R)
S02 . a is Element of the carrier of R
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S02 . n is Element of the carrier of R
b is finite Element of Fin the carrier of R
(R,b) is Element of the carrier of R
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
(S01 ^\ (S02 mindex (R,(rng S02)))) . n is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . n) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . n)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . n) is non empty cup-closed diff-closed preBoolean set
b0 . n is Element of the carrier of (R)
b0 . a is Element of the carrier of (R)
(S01 ^\ (S02 mindex (R,(rng S02)))) . a is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . a) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a) is non empty cup-closed diff-closed preBoolean set
b is finite Element of Fin the carrier of R
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b0 . a is Element of the carrier of (R)
(S01 ^\ (S02 mindex (R,(rng S02)))) . a is Element of the carrier of (R)
((S01 ^\ (S02 mindex (R,(rng S02)))) . a) \ {(R,(rng S02))} is Element of bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a)
bool ((S01 ^\ (S02 mindex (R,(rng S02)))) . a) is non empty cup-closed diff-closed preBoolean set
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 . a is Element of the carrier of R
the Element of the carrier of R is Element of the carrier of R
[ the Element of the carrier of R,A] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
[: the carrier of R,(bool [:NAT, the carrier of (R):]):] is non empty non trivial Relation-like non finite set
{ the Element of the carrier of R,A} is non empty finite set
{ the Element of the carrier of R} is non empty trivial finite 1 -element set
{{ the Element of the carrier of R,A},{ the Element of the carrier of R}} is non empty finite V34() set
SS is Element of [: the carrier of R,zz:]
SS `2 is Element of zz
S02 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S0max is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
a0 is Element of the carrier of R
rng S0max is non empty set
(R,(rng S0max)) is Element of the carrier of R
i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S0max mindex a0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
b0t is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S02 ^\ i0 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
b0 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{a0} is non empty trivial finite 1 -element Element of bool the carrier of R
bool the carrier of R is non empty cup-closed diff-closed preBoolean set
S01 is Element of [: the carrier of R,zz:]
[a0,b0] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
{a0,b0} is non empty finite set
{a0} is non empty trivial finite 1 -element set
{{a0,b0},{a0}} is non empty finite V34() set
[:NAT,[: the carrier of R,zz:]:] is non empty non trivial Relation-like non finite set
bool [:NAT,[: the carrier of R,zz:]:] is non empty non trivial non finite cup-closed diff-closed preBoolean set
S is non empty Relation-like NAT -defined [: the carrier of R,zz:] -valued Function-like total V18( NAT ,[: the carrier of R,zz:]) Element of bool [:NAT,[: the carrier of R,zz:]:]
S . 0 is Element of [: the carrier of R,zz:]
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . a is Element of [: the carrier of R,zz:]
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S . (a + 1) is Element of [: the carrier of R,zz:]
(S . a) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
S . a is Element of [: the carrier of R,zz:]
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S . (a + 1) is Element of [: the carrier of R,zz:]
(S . a) `2 is set
n is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
b is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
i is Element of the carrier of R
rng b is non empty set
(R,(rng b)) is Element of the carrier of R
n1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b mindex i is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
n ^\ n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
Sn12 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{i} is non empty trivial finite 1 -element Element of bool the carrier of R
[i,Sn12] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
{i,Sn12} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,Sn12},{i}} is non empty finite V34() set
a is set
a is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . a is Element of [: the carrier of R,zz:]
n is Element of [: the carrier of R,zz:]
n `1 is Element of the carrier of R
S . a is set
(S . a) `1 is set
a is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
(S . 0) `2 is Element of zz
(S . 0) `1 is Element of the carrier of R
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i . n is Element of the carrier of (R)
n1 is set
[n1,((S . 0) `1)] is V1() set
{n1,((S . 0) `1)} is non empty finite set
{n1} is non empty trivial finite 1 -element set
{{n1,((S . 0) `1)},{n1}} is non empty finite V34() set
[a0,b0] `1 is Element of the carrier of R
[a0,b0] `2 is Relation-like NAT -defined the carrier of (R) -valued Element of bool [:NAT, the carrier of (R):]
b0t . n is Element of the carrier of (R)
(b0t . n) \ {a0} is Element of bool (b0t . n)
bool (b0t . n) is non empty cup-closed diff-closed preBoolean set
n + i0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S02 . (n + i0) is Element of the carrier of (R)
S0max . (n + i0) is Element of the carrier of R
Sn12 is finite Element of Fin the carrier of R
(R,Sn12) is Element of the carrier of R
[a0,n1] is V1() set
{a0,n1} is non empty finite set
{{a0,n1},{a0}} is non empty finite V34() set
n1 is Element of the carrier of R
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . n is Element of [: the carrier of R,zz:]
(S . n) `2 is Element of zz
(S . n) `1 is Element of the carrier of R
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S . (n + 1) is Element of [: the carrier of R,zz:]
(S . (n + 1)) `2 is Element of zz
(S . (n + 1)) `1 is Element of the carrier of R
b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . n1 is Element of [: the carrier of R,zz:]
(S . n1) `2 is Element of zz
Sn12 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
Sn1max is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
an1 is Element of the carrier of R
rng Sn1max is non empty set
(R,(rng Sn1max)) is Element of the carrier of R
in1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Sn1max mindex an1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
bn1t is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
Sn12 ^\ in1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
bn1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{an1} is non empty trivial finite 1 -element Element of bool the carrier of R
[an1,bn1] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
{an1,bn1} is non empty finite set
{an1} is non empty trivial finite 1 -element set
{{an1,bn1},{an1}} is non empty finite V34() set
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i . b is Element of the carrier of (R)
i is set
[i,((S . (n + 1)) `1)] is V1() set
{i,((S . (n + 1)) `1)} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,((S . (n + 1)) `1)},{i}} is non empty finite V34() set
[an1,bn1] `1 is Element of the carrier of R
[an1,bn1] `2 is Relation-like NAT -defined the carrier of (R) -valued Element of bool [:NAT, the carrier of (R):]
bn1t . b is Element of the carrier of (R)
(bn1t . b) \ {an1} is Element of bool (bn1t . b)
bool (bn1t . b) is non empty cup-closed diff-closed preBoolean set
b + in1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Sn12 . (b + in1) is Element of the carrier of (R)
Sn1max . (b + in1) is Element of the carrier of R
Sn2ib is finite Element of Fin the carrier of R
(R,Sn2ib) is Element of the carrier of R
[an1,i] is V1() set
{an1,i} is non empty finite set
{{an1,i},{an1}} is non empty finite V34() set
c36 is Element of the carrier of R
a is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . (0 + 1) is Element of the carrier of R
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
b is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
S . (0 + 1) is Element of [: the carrier of R,zz:]
(S . (0 + 1)) `1 is Element of the carrier of R
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
n1 is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
n1 is Element of the carrier of R
rng n1 is non empty set
(R,(rng n1)) is Element of the carrier of R
Sn12 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n1 mindex n1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
Sn1max is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i ^\ Sn12 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
an1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{n1} is non empty trivial finite 1 -element Element of bool the carrier of R
[n1,an1] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
{n1,an1} is non empty finite set
{n1} is non empty trivial finite 1 -element set
{{n1,an1},{n1}} is non empty finite V34() set
dom n1 is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
in1 is set
n1 . in1 is set
i . in1 is set
bn1t is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b . bn1t is Element of the carrier of (R)
bn1 is finite Element of Fin the carrier of R
(R,bn1) is Element of the carrier of R
[n1,an1] `1 is Element of the carrier of R
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . n is Element of [: the carrier of R,zz:]
(S . n) `2 is Element of zz
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . (n + 1) is Element of the carrier of R
S . (n + 1) is Element of [: the carrier of R,zz:]
(S . (n + 1)) `2 is Element of zz
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . ((n + 1) + 1) is Element of the carrier of R
n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
n1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
S . n1 is Element of [: the carrier of R,zz:]
(S . n1) `2 is Element of zz
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
S . (n1 + 1) is Element of [: the carrier of R,zz:]
Sn12 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
Sn1max is non empty Relation-like NAT -defined the carrier of R -valued Function-like total V18( NAT , the carrier of R) Element of bool [:NAT, the carrier of R:]
an1 is Element of the carrier of R
rng Sn1max is non empty set
(R,(rng Sn1max)) is Element of the carrier of R
in1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
Sn1max mindex an1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real non negative V49() V72() V73() V74() V75() V76() V77() V295() V296() V297() Element of NAT
bn1t is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
Sn12 ^\ in1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
bn1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
{an1} is non empty trivial finite 1 -element Element of bool the carrier of R
[an1,bn1] is V1() Element of [: the carrier of R,(bool [:NAT, the carrier of (R):]):]
{an1,bn1} is non empty finite set
{an1} is non empty trivial finite 1 -element set
{{an1,bn1},{an1}} is non empty finite V34() set
dom Sn1max is non empty V72() V73() V74() V75() V76() V77() V293() V295() Element of bool NAT
i is set
Sn1max . i is set
Sn12 . i is set
i is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
i . i is Element of the carrier of (R)
c36 is finite Element of Fin the carrier of R
(R,c36) is Element of the carrier of R
[an1,bn1] `1 is Element of the carrier of R
a . 0 is Element of the carrier of R
[(a . (0 + 1)),(a . 0)] is V1() Element of [: the carrier of R, the carrier of R:]
{(a . (0 + 1)),(a . 0)} is non empty finite set
{(a . (0 + 1))} is non empty trivial finite 1 -element set
{{(a . (0 + 1)),(a . 0)},{(a . (0 + 1))}} is non empty finite V34() set
n is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n . b is Element of the carrier of (R)
n is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
b is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n . b is Element of the carrier of (R)
i is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i . b is Element of the carrier of (R)
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . (n + 1) is Element of the carrier of R
a . n is Element of the carrier of R
[(a . (n + 1)),(a . n)] is V1() Element of [: the carrier of R, the carrier of R:]
{(a . (n + 1)),(a . n)} is non empty finite set
{(a . (n + 1))} is non empty trivial finite 1 -element set
{{(a . (n + 1)),(a . n)},{(a . (n + 1))}} is non empty finite V34() set
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . ((n + 1) + 1) is Element of the carrier of R
[(a . ((n + 1) + 1)),(a . (n + 1))] is V1() Element of [: the carrier of R, the carrier of R:]
{(a . ((n + 1) + 1)),(a . (n + 1))} is non empty finite set
{(a . ((n + 1) + 1))} is non empty trivial finite 1 -element set
{{(a . ((n + 1) + 1)),(a . (n + 1))},{(a . ((n + 1) + 1))}} is non empty finite V34() set
S . (n + 1) is Element of [: the carrier of R,zz:]
(S . (n + 1)) `1 is Element of the carrier of R
(S . (n + 1)) `2 is Element of zz
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() V44() ext-real positive non negative V49() V72() V73() V74() V75() V76() V77() V293() V294() V295() V296() V297() Element of NAT
a . ((n + 1) + 1) is Element of the carrier of R
b is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
i is epsilon-transitive epsilon-connected ordinal natural finite cardinal V42() V43() ext-real non negative set
b . i is Element of the carrier of (R)
n1 is non empty Relation-like NAT -defined the carrier of (R) -valued Function-like total V18( NAT , the carrier of (R)) Element of bool [:NAT, the carrier of (R):]
n1 . i is Element of the carrier of (R)