REAL is set
NAT is non empty V12() V29() V30() V31() non finite cardinal limit_cardinal Element of K19(REAL)
K19(REAL) is cup-closed diff-closed preBoolean set
{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered set
COMPLEX is set
NAT is non empty V12() V29() V30() V31() non finite cardinal limit_cardinal set
K19(NAT) is V12() cup-closed diff-closed preBoolean non finite set
K19(NAT) is V12() cup-closed diff-closed preBoolean non finite set
Fin NAT is non empty cup-closed diff-closed preBoolean set
INT is set
1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
2 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
3 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT
Seg 1 is non empty V12() finite 1 -element Element of K19(NAT)
{1} is non empty V12() finite V47() 1 -element set
Seg 2 is non empty finite 2 -element Element of K19(NAT)
{1,2} is non empty finite V47() set
K is non empty Abelian addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
the addF of K . (a1,a2) is Element of the carrier of K
a1 + a2 is Element of the carrier of K
the addF of K . (a2,a1) is Element of the carrier of K
K is non empty add-associative addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
b1 is Element of the carrier of K
the addF of K . (a2,b1) is Element of the carrier of K
the addF of K . (a1,( the addF of K . (a2,b1))) is Element of the carrier of K
a2 + b1 is Element of the carrier of K
a1 + (a2 + b1) is Element of the carrier of K
the addF of K . (a1,(a2 + b1)) is Element of the carrier of K
a1 + a2 is Element of the carrier of K
the addF of K . (a1,a2) is Element of the carrier of K
(a1 + a2) + b1 is Element of the carrier of K
the addF of K . ((a1 + a2),b1) is Element of the carrier of K
the addF of K . (( the addF of K . (a1,a2)),b1) is Element of the carrier of K
K is non empty commutative multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
a1 * a2 is Element of the carrier of K
a2 * a1 is Element of the carrier of K
the multF of K . (a2,a1) is Element of the carrier of K
K is non empty Abelian addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
K is non empty add-associative addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
K is non empty commutative multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
K is non empty unital commutative right_unital left_unital multLoopStr
the carrier of K is non empty set
1. K is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a2 is Element of the carrier of K
the multF of K . ((1. K),a2) is Element of the carrier of K
(1. K) * a2 is Element of the carrier of K
the multF of K . (a2,(1. K)) is Element of the carrier of K
a2 * (1. K) is Element of the carrier of K
K is non empty unital commutative right_unital left_unital multLoopStr
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the_unity_wrt the multF of K is Element of the carrier of K
1. K is Element of the carrier of K
a1 is Element of the carrier of K
K is non empty left_zeroed right_zeroed addLoopStr
the carrier of K is non empty set
0. K is V63(K) Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
the addF of K . ((0. K),a1) is Element of the carrier of K
(0. K) + a1 is Element of the carrier of K
the addF of K . (a1,(0. K)) is Element of the carrier of K
a1 + (0. K) is Element of the carrier of K
K is non empty left_zeroed right_zeroed addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the_unity_wrt the addF of K is Element of the carrier of K
0. K is V63(K) Element of the carrier of K
a1 is Element of the carrier of K
K is non empty left_zeroed right_zeroed addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
0. K is V63(K) Element of the carrier of K
K is non empty unital commutative right_unital left_unital multLoopStr
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
K is non empty right-distributive left-distributive distributive doubleLoopStr
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
a1 is Element of the carrier of K
a2 is Element of the carrier of K
b1 is Element of the carrier of K
the addF of K . (a2,b1) is Element of the carrier of K
the multF of K . (a1,( the addF of K . (a2,b1))) is Element of the carrier of K
a2 + b1 is Element of the carrier of K
a1 * (a2 + b1) is Element of the carrier of K
the multF of K . (a1,(a2 + b1)) is Element of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
a1 * b1 is Element of the carrier of K
the multF of K . (a1,b1) is Element of the carrier of K
(a1 * a2) + (a1 * b1) is Element of the carrier of K
the addF of K . ((a1 * a2),(a1 * b1)) is Element of the carrier of K
the addF of K . (( the multF of K . (a1,a2)),( the multF of K . (a1,b1))) is Element of the carrier of K
the addF of K . (a1,a2) is Element of the carrier of K
the multF of K . (( the addF of K . (a1,a2)),b1) is Element of the carrier of K
a1 + a2 is Element of the carrier of K
(a1 + a2) * b1 is Element of the carrier of K
the multF of K . ((a1 + a2),b1) is Element of the carrier of K
a2 * b1 is Element of the carrier of K
the multF of K . (a2,b1) is Element of the carrier of K
(a1 * b1) + (a2 * b1) is Element of the carrier of K
the addF of K . ((a1 * b1),(a2 * b1)) is Element of the carrier of K
the addF of K . (( the multF of K . (a1,b1)),( the multF of K . (a2,b1))) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K is non empty addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the addF of K * ((id the carrier of K),(comp K)) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K is non empty addLoopStr
the carrier of K is non empty set
(K) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the addF of K * ((id the carrier of K),(comp K)) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
a1 is Element of the carrier of K
a2 is Element of the carrier of K
(K) . (a1,a2) is Element of the carrier of K
a1 - a2 is Element of the carrier of K
- a2 is Element of the carrier of K
a1 + (- a2) is Element of the carrier of K
the addF of K . (a1,(- a2)) is Element of the carrier of K
(comp K) . a2 is Element of the carrier of K
the addF of K . (a1,((comp K) . a2)) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
a2 is Element of the carrier of K
the multF of K [;] (a2,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
a1 is Element of the carrier of K
( the multF of K [;] (a2,(id the carrier of K))) . a1 is Element of the carrier of K
a2 * a1 is Element of the carrier of K
the multF of K . (a2,a1) is Element of the carrier of K
(id the carrier of K) . a1 is Element of the carrier of K
the multF of K . (a2,((id the carrier of K) . a1)) is Element of the carrier of K
K is non empty right-distributive left-distributive distributive doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
(K,a1) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of K is non empty set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
(comp K) . a1 is Element of the carrier of K
the addF of K . (a1,((comp K) . a1)) is Element of the carrier of K
- a1 is Element of the carrier of K
a1 + (- a1) is Element of the carrier of K
the addF of K . (a1,(- a1)) is Element of the carrier of K
0. K is V63(K) Element of the carrier of K
the_unity_wrt the addF of K is Element of the carrier of K
the addF of K . (((comp K) . a1),a1) is Element of the carrier of K
(- a1) + a1 is Element of the carrier of K
the addF of K . ((- a1),a1) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the_inverseOp_wrt the addF of K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of K is non empty set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the_inverseOp_wrt the addF of K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K is non empty addLoopStr
the carrier of K is non empty set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the addF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
p is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
dom (K,a1,a2) is finite Element of K19(NAT)
b1 is Element of the carrier of K
a1 . p is set
b2 is Element of the carrier of K
a2 . p is set
(K,a1,a2) . p is set
b1 + b2 is Element of the carrier of K
the addF of K . (b1,b2) is Element of the carrier of K
a1 is non empty addLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg K is finite K -element Element of K19(NAT)
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a2 is non empty addLoopStr
the carrier of a2 is non empty set
K -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
b1 is Element of the carrier of a2
b2 is Element of the carrier of a2
b1 + b2 is Element of the carrier of a2
the addF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the addF of a2 . (b1,b2) is Element of the carrier of a2
p is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a2
p . a1 is set
q is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a2
q . a1 is set
(K,a2,p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a2
the addF of a2 .: (p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a2
(K,a2,p,q) . a1 is set
len (K,a2,p,q) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len (K,a2,p,q)) is finite len (K,a2,p,q) -element Element of K19(NAT)
dom (K,a2,p,q) is finite K -element Element of K19(NAT)
K is non empty addLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Element of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(1,K,<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K .: (<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 + a2 is Element of the carrier of K
the addF of K . (a1,a2) is Element of the carrier of K
<*(a1 + a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
a1 is non empty addLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Element of the carrier of a1
K |-> b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: ((K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 + b1 is Element of the carrier of a1
the addF of a1 . (a2,b1) is Element of the carrier of a1
K |-> (a2 + b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_zeroed right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the_unity_wrt the addF of a1 is Element of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_zeroed Abelian right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K |-> (0. a1)),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K |-> (0. a1)),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is non empty addLoopStr
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
(comp K) * a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty addLoopStr
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
- a2 is Element of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
dom (a1,b1) is finite Element of K19(NAT)
b1 . K is set
(a1,b1) . K is set
(comp a1) . a2 is Element of the carrier of a1
a1 is non empty addLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg a1 is finite a1 -element Element of K19(NAT)
a2 is non empty addLoopStr
the carrier of a2 is non empty set
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
b1 is Element of the carrier of a2
- b1 is Element of the carrier of a2
b2 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
b2 . K is set
(a1,a2,b2) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
comp a2 is Relation-like Function-like non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K19(K20( the carrier of a2, the carrier of a2)) is cup-closed diff-closed preBoolean set
(comp a2) * b2 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a2
(a1,a2,b2) . K is set
len (a1,a2,b2) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len (a1,a2,b2)) is finite len (a1,a2,b2) -element Element of K19(NAT)
dom (a1,a2,b2) is finite a1 -element Element of K19(NAT)
K is non empty addLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
(1,K,<*a1*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
(comp K) * <*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- a1 is Element of the carrier of K
<*(- a1)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(comp K) . a1 is Element of the carrier of K
<*((comp K) . a1)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty addLoopStr
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
(K,a1,(K |-> a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * (K |-> a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
- a2 is Element of the carrier of a1
K |-> (- a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) . a2 is Element of the carrier of a1
K |-> ((comp a1) . a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the_inverseOp_wrt the addF of a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(the_inverseOp_wrt the addF of a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the addF of a1 .: (a2,((the_inverseOp_wrt the addF of a1) * a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the_unity_wrt the addF of a1 is Element of the carrier of a1
K |-> (the_unity_wrt the addF of a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the_inverseOp_wrt the addF of a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the_unity_wrt the addF of a1 is Element of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b2,b1),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b2,b1),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,(K,a1,b1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b2,(K,a1,b1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * (K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),(K,a1,(K,a1,a2),(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),(K,a1,(K,a1,a2),(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,(K,a1,a2,b1),(K,a1,a2)),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,(K,a1,a2,b1),(K,a1,a2)),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,a2),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1,a2),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,(K,a1,b1,a2),(K,a1,a2)),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,(K,a1,b1,a2),(K,a1,a2)),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,a2,(K,a1,a2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K,a1,a2,(K,a1,a2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,(K,a1,a2,(K,a1,a2))),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1,(K,a1,a2,(K,a1,a2))),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,(K |-> (0. a1))),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1,(K |-> (0. a1))),(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is non empty addLoopStr
the carrier of K is non empty set
(K) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the addF of K * ((id the carrier of K),(comp K)) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K) .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty addLoopStr
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
a2 - b1 is Element of the carrier of a1
- b1 is Element of the carrier of a1
a2 + (- b1) is Element of the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 . (a2,(- b1)) is Element of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 . K is set
p is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,b2,p) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (b2,p) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
dom (a1,b2,p) is finite Element of K19(NAT)
p . K is set
(a1,b2,p) . K is set
(a1) . (a2,b1) is Element of the carrier of a1
a1 is non empty addLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg a1 is finite a1 -element Element of K19(NAT)
a2 is non empty addLoopStr
the carrier of a2 is non empty set
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
b1 is Element of the carrier of a2
b2 is Element of the carrier of a2
b1 - b2 is Element of the carrier of a2
- b2 is Element of the carrier of a2
b1 + (- b2) is Element of the carrier of a2
the addF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the addF of a2 . (b1,(- b2)) is Element of the carrier of a2
p is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
p . K is set
q is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
q . K is set
(a1,a2,p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
(a2) is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
id the carrier of a2 is Relation-like the carrier of a2 -defined the carrier of a2 -valued Function-like one-to-one non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
K19(K20( the carrier of a2, the carrier of a2)) is cup-closed diff-closed preBoolean set
comp a2 is Relation-like Function-like non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
the addF of a2 * ((id the carrier of a2),(comp a2)) is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
(a2) .: (p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a2
(a1,a2,p,q) . K is set
len (a1,a2,p,q) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len (a1,a2,p,q)) is finite len (a1,a2,p,q) -element Element of K19(NAT)
dom (a1,a2,p,q) is finite a1 -element Element of K19(NAT)
K is non empty addLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Element of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(1,K,<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(K) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the addF of K * ((id the carrier of K),(comp K)) is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
(K) .: (<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 - a2 is Element of the carrier of K
- a2 is Element of the carrier of K
a1 + (- a2) is Element of the carrier of K
the addF of K . (a1,(- a2)) is Element of the carrier of K
<*(a1 - a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(K) . (a1,a2) is Element of the carrier of K
<*((K) . (a1,a2))*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty addLoopStr
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Element of the carrier of a1
K |-> b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: ((K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 - b1 is Element of the carrier of a1
- b1 is Element of the carrier of a1
a2 + (- b1) is Element of the carrier of a1
the addF of a1 . (a2,(- b1)) is Element of the carrier of a1
K |-> (a2 - b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) . (a2,b1) is Element of the carrier of a1
K |-> ((a1) . (a2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K |-> (0. a1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K |-> (0. a1)))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K |-> (0. a1)))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
- (0. a1) is Element of the carrier of a1
K |-> (- (0. a1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (- (0. a1)))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K |-> (- (0. a1)))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_zeroed Abelian right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> (0. a1)),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: ((K |-> (0. a1)),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K |-> (0. a1)),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K |-> (0. a1)),(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: (b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2),(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2),(K,a1,(K,a1,b1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: ((K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: (a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,(K,a1,b1)),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,(K,a1,b1)),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1),(K,a1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1),(K,a1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: ((K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (b1,(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,(K,a1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1,(K,a1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),(K,a1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: (a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * (K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1,b2))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1),b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1),b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,(K,a1,b1)),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,(K,a1,b1)),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: ((K,a1,a2,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) .: (b1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K |-> (0. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(comp a1) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,(K,a1,b1),b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,(K,a1,b1),b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: (a2,(K,a1,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,(K,a1,b1)),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,a2,(K,a1,b1)),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is non empty multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Element of the carrier of K
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
a2 is Element of the carrier of K
( the multF of K [;] (a1,(id the carrier of K))) . a2 is Element of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
(id the carrier of K) . a2 is Element of the carrier of K
the multF of K . (a1,((id the carrier of K) . a2)) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
a1 is Element of the carrier of K
(K,a1) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
a2 is Element of the carrier of K
(K,a1) . a2 is Element of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Element of the carrier of K
(K,a2) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the multF of K [;] (a2,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
(K,a2) * a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty multMagma
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
a2 * b1 is Element of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 . (a2,b1) is Element of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
dom (a1,b2,a2) is finite Element of K19(NAT)
b2 . K is set
(a1,b2,a2) . K is set
dom ( the multF of a1 [;] (a2,(id the carrier of a1))) is non empty set
( the multF of a1 [;] (a2,(id the carrier of a1))) . b1 is Element of the carrier of a1
(id the carrier of a1) . b1 is Element of the carrier of a1
the multF of a1 . (a2,((id the carrier of a1) . b1)) is Element of the carrier of a1
a1 is non empty multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Element of the carrier of a1
(a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,b1) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (b1,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,b1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg a1 is finite a1 -element Element of K19(NAT)
a2 is non empty multMagma
the carrier of a2 is non empty set
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
b1 is Element of the carrier of a2
b2 is Element of the carrier of a2
b2 * b1 is Element of the carrier of a2
the multF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the multF of a2 . (b2,b1) is Element of the carrier of a2
p is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
p . K is set
(a1,a2,p,b2) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
(a2,b2) is Relation-like Function-like non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
K19(K20( the carrier of a2, the carrier of a2)) is cup-closed diff-closed preBoolean set
id the carrier of a2 is Relation-like the carrier of a2 -defined the carrier of a2 -valued Function-like one-to-one non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
the multF of a2 [;] (b2,(id the carrier of a2)) is Relation-like Function-like non empty total V18( the carrier of a2, the carrier of a2) Element of K19(K20( the carrier of a2, the carrier of a2))
(a2,b2) * p is Relation-like NAT -defined the carrier of a2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a2
(a1,a2,p,b2) . K is set
len (a1,a2,p,b2) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len (a1,a2,p,b2)) is finite len (a1,a2,p,b2) -element Element of K19(NAT)
dom (a1,a2,p,b2) is finite a1 -element Element of K19(NAT)
K is non empty multMagma
the carrier of K is non empty set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
(1,K,<*a2*>,a1) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(K,a1) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
(K,a1) * <*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
<*(a1 * a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
( the multF of K [;] (a1,(id the carrier of K))) . a2 is Element of the carrier of K
<*(( the multF of K [;] (a1,(id the carrier of K))) . a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty multMagma
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
K |-> b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
(K,a1,(K |-> b1),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * (K |-> b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 * b1 is Element of the carrier of a1
the multF of a1 . (a2,b1) is Element of the carrier of a1
K |-> (a2 * b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
( the multF of a1 [;] (a2,(id the carrier of a1))) . b1 is Element of the carrier of a1
K |-> (( the multF of a1 [;] (a2,(id the carrier of a1))) . b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty associative multMagma
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
a2 * b1 is Element of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 . (a2,b1) is Element of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b2,(a2 * b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,(a2 * b1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] ((a2 * b1),(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,(a2 * b1)) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,b1) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (b1,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,b1) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b2,b1),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * (K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 [;] (a2,( the multF of a1 [;] (b1,(id the carrier of a1)))) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
( the multF of a1 [;] (a2,( the multF of a1 [;] (b1,(id the carrier of a1))))) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
( the multF of a1 [;] (a2,(id the carrier of a1))) * ( the multF of a1 [;] (b1,(id the carrier of a1))) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(( the multF of a1 [;] (a2,(id the carrier of a1))) * ( the multF of a1 [;] (b1,(id the carrier of a1)))) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty right-distributive left-distributive distributive doubleLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
a2 + b1 is Element of the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 . (a2,b1) is Element of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b2,(a2 + b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,(a2 + b1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] ((a2 + b1),(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,(a2 + b1)) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,b1) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (b1,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,b1) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b2,a2),(K,a1,b2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b2,a2),(K,a1,b2,b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the addF of a1 .: (( the multF of a1 [;] (a2,(id the carrier of a1))),( the multF of a1 [;] (b1,(id the carrier of a1)))) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
( the addF of a1 .: (( the multF of a1 [;] (a2,(id the carrier of a1))),( the multF of a1 [;] (b1,(id the carrier of a1))))) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a1 is non empty right-distributive left-distributive distributive doubleLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 is Element of the carrier of a1
(K,a1,(K,a1,b1,b2),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * (K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,a2),(K,a1,b2,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 .: ((K,a1,b1,a2),(K,a1,b2,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty unital commutative right-distributive left-distributive right_unital distributive left_unital doubleLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
1. a1 is Element of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(1. a1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,(1. a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] ((1. a1),(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,(1. a1)) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
rng a2 is finite set
the_unity_wrt the multF of a1 is Element of the carrier of a1
(id the carrier of a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed right-distributive left-distributive distributive doubleLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
0. a1 is V63(a1) Element of the carrier of a1
K |-> (0. a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(0. a1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,(0. a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] ((0. a1),(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,(0. a1)) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
rng a2 is finite set
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
the_unity_wrt the addF of a1 is Element of the carrier of a1
(id the carrier of a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 [;] ((0. a1),((id the carrier of a1) * a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 [;] ((0. a1),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like unital commutative add-associative right_zeroed right-distributive left-distributive right_unital distributive left_unital doubleLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
1. a1 is Element of the carrier of a1
- (1. a1) is Element of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,(- (1. a1))) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,(- (1. a1))) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] ((- (1. a1)),(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,(- (1. a1))) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(comp a1) * a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(comp a1) . (1. a1) is Element of the carrier of a1
the_unity_wrt the multF of a1 is Element of the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
the_inverseOp_wrt the addF of a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K is non empty multMagma
the carrier of K is non empty set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 is non empty multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
p is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(a1,b2,p) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (b2,p) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
dom (a1,b2,p) is finite Element of K19(NAT)
a2 is Element of the carrier of a1
b2 . K is set
b1 is Element of the carrier of a1
p . K is set
(a1,b2,p) . K is set
a2 * b1 is Element of the carrier of a1
the multF of a1 . (a2,b1) is Element of the carrier of a1
a1 is non empty multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg a1 is finite a1 -element Element of K19(NAT)
a2 is non empty multMagma
the carrier of a2 is non empty set
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
b1 is Element of the carrier of a2
b2 is Element of the carrier of a2
b1 * b2 is Element of the carrier of a2
the multF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the multF of a2 . (b1,b2) is Element of the carrier of a2
p is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
p . K is set
q is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
q . K is set
(a1,a2,p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
the multF of a2 .: (p,q) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a2
(a1,a2,p,q) . K is set
len (a1,a2,p,q) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len (a1,a2,p,q)) is finite len (a1,a2,p,q) -element Element of K19(NAT)
dom (a1,a2,p,q) is finite a1 -element Element of K19(NAT)
K is non empty multMagma
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Element of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(1,K,<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
<*(a1 * a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
K is non empty multMagma
the carrier of K is non empty set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
<*a1,a2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
b1 is Element of the carrier of K
a1 * b1 is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K . (a1,b1) is Element of the carrier of K
b2 is Element of the carrier of K
<*b1,b2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,<*a1,a2*>,<*b1,b2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K .: (<*a1,a2*>,<*b1,b2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 * b2 is Element of the carrier of K
the multF of K . (a2,b2) is Element of the carrier of K
<*(a1 * b1),(a2 * b2)*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
<*a1*> ^ <*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
1 + 1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
<*b1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
<*b2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
<*b1*> ^ <*b2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(1,K,<*a1*>,<*b1*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
the multF of K .: (<*a1*>,<*b1*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*(a2 * b2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(1,K,<*a1*>,<*b1*>) ^ <*(a2 * b2)*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*(a1 * b1)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
<*(a1 * b1)*> ^ <*(a2 * b2)*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 is non empty commutative multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is non empty commutative multMagma
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a2,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K .: (a2,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
len a2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
min ((len a1),(len a2)) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
b1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len b1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
dom b1 is finite Element of K19(NAT)
p is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg p is finite p -element Element of K19(NAT)
Seg (len a2) is finite len a2 -element Element of K19(NAT)
dom a2 is finite Element of K19(NAT)
Seg (len a1) is finite len a1 -element Element of K19(NAT)
dom a1 is finite Element of K19(NAT)
b2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len b2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
min ((len a2),(len a1)) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
dom b2 is finite Element of K19(NAT)
q is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
a1 . q is set
a2 . q is set
b1 . q is set
q is Element of the carrier of K
px is Element of the carrier of K
q * px is Element of the carrier of K
the multF of K . (q,px) is Element of the carrier of K
px * q is Element of the carrier of K
the multF of K . (px,q) is Element of the carrier of K
b2 . q is set
a1 is non empty associative multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (a2,(K,a1,b1,b2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K,a1,a2,b1),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty associative commutative multMagma
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: ((K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K |-> a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (b1,(K |-> a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
the multF of a1 [;] (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty associative commutative multMagma
the carrier of a1 is non empty set
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Element of the carrier of a1
K |-> b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: ((K |-> a2),(K |-> b1)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 * b1 is Element of the carrier of a1
the multF of a1 . (a2,b1) is Element of the carrier of a1
K |-> (a2 * b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> b1),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * (K |-> b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a1 is non empty associative multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a2 is Element of the carrier of a1
(K,a1,(K,a1,b1,b2),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * (K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,a2),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K,a1,b1,a2),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty associative commutative multMagma
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Element of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,b2),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * (K,a1,b1,b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b1,a2),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K,a1,b1,a2),b2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * b2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b1,(K,a1,b2,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (b1,(K,a1,b2,a2)) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: (b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b2,b1),a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) * (K,a1,b2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
(K,a1,(K,a1,b2,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K,a1,b2,a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
a1 is non empty associative commutative multMagma
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
a2 is Element of the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,(K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
K is non empty addLoopStr
the carrier of K is non empty set
0. K is V63(K) Element of the carrier of K
a1 is Element of the carrier of K
(0. K) + a1 is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K . ((0. K),a1) is Element of the carrier of K
a1 + (0. K) is Element of the carrier of K
the addF of K . (a1,(0. K)) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum a1 is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K "**" a1 is Element of the carrier of K
<*> the carrier of K is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
b1 is Element of the carrier of K
K20(NAT, the carrier of K) is Relation-like V12() non finite set
K19(K20(NAT, the carrier of K)) is V12() cup-closed diff-closed preBoolean non finite set
b2 is Relation-like Function-like non empty total V18( NAT , the carrier of K) Element of K19(K20(NAT, the carrier of K))
p is finite Element of Fin NAT
a1 | p is Relation-like NAT -defined p -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | p) is finite set
Sgm (dom (a1 | p)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom (a1 | p))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
dom a1 is finite Element of K19(NAT)
Sum (<*> the carrier of K) is Element of the carrier of K
q is Element of the carrier of K
q is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q is Element of the carrier of K
dom a1 is finite Element of K19(NAT)
q is non empty set
K20(q, the carrier of K) is Relation-like set
K19(K20(q, the carrier of K)) is cup-closed diff-closed preBoolean set
px is Relation-like NAT -defined Function-like FinSubsequence-like set
dom px is set
Sgm (dom px) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom px)) is finite set
e is Relation-like NAT -defined q -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of q
q is Relation-like Function-like non empty total V18(q, the carrier of K) Element of K19(K20(q, the carrier of K))
q * e is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
f4 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum f4 is Element of the carrier of K
Y is Element of the carrier of K
dom a1 is finite Element of K19(NAT)
K20((Fin NAT), the carrier of K) is Relation-like set
K19(K20((Fin NAT), the carrier of K)) is cup-closed diff-closed preBoolean set
p is Relation-like Function-like non empty total V18( Fin NAT, the carrier of K) Element of K19(K20((Fin NAT), the carrier of K))
q is finite Element of Fin NAT
dom a1 is finite Element of K19(NAT)
q is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
{q} is non empty V12() finite V47() 1 -element set
q \/ {q} is non empty finite set
a1 | (q \/ {q}) is Relation-like NAT -defined q \/ {q} -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | (q \/ {q})) is finite set
Sgm (dom (a1 | (q \/ {q}))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom (a1 | (q \/ {q})))) -| q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(Sgm (dom (a1 | (q \/ {q})))) |-- q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Sgm (dom (a1 | (q \/ {q})))) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
finSeg (len (Sgm (dom (a1 | (q \/ {q}))))) is finite len (Sgm (dom (a1 | (q \/ {q})))) -element Element of Fin NAT
(Sgm (dom (a1 | (q \/ {q})))) " {q} is finite set
(finSeg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}) is finite Element of K19((finSeg (len (Sgm (dom (a1 | (q \/ {q})))))))
K19((finSeg (len (Sgm (dom (a1 | (q \/ {q}))))))) is cup-closed diff-closed preBoolean finite V47() set
Seg (len (Sgm (dom (a1 | (q \/ {q}))))) is finite len (Sgm (dom (a1 | (q \/ {q})))) -element Element of K19(NAT)
dom (Sgm (dom (a1 | (q \/ {q})))) is finite Element of K19(NAT)
Y is finite set
(Sgm (dom (a1 | (q \/ {q})))) | Y is Relation-like NAT -defined Y -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT,NAT))
K20(NAT,NAT) is Relation-like V12() non finite set
K19(K20(NAT,NAT)) is V12() cup-closed diff-closed preBoolean non finite set
rng ((Sgm (dom (a1 | (q \/ {q})))) | Y) is finite set
Sgm Y is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom (a1 | (q \/ {q})))) * (Sgm Y) is Relation-like NAT -defined NAT -valued Function-like finite Element of K19(K20(NAT,NAT))
rng (Sgm Y) is finite set
dom (Sgm Y) is finite Element of K19(NAT)
card Y is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
finSeg (card Y) is finite card Y -element Element of Fin NAT
dom ((Sgm (dom (a1 | (q \/ {q})))) * (Sgm Y)) is finite set
Seg (card Y) is finite card Y -element Element of K19(NAT)
rng (Sgm (dom (a1 | (q \/ {q})))) is finite set
M is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng M is finite set
pB9x is set
L is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng L is finite set
dom L is finite Element of K19(NAT)
pp is set
L . pp is set
(Sgm Y) . pp is set
(Sgm (dom (a1 | (q \/ {q})))) . ((Sgm Y) . pp) is set
dom ((Sgm (dom (a1 | (q \/ {q})))) | Y) is finite set
pp is set
((Sgm (dom (a1 | (q \/ {q})))) | Y) . pp is set
(dom (Sgm (dom (a1 | (q \/ {q}))))) /\ Y is finite Element of K19(NAT)
D is set
(Sgm Y) . D is set
L . D is set
(Sgm (dom (a1 | (q \/ {q})))) . ((Sgm Y) . D) is set
(dom a1) /\ (q \/ {q}) is finite Element of K19(NAT)
len a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len a1) is finite len a1 -element Element of K19(NAT)
a1 | q is Relation-like NAT -defined q -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | q) is finite set
(dom a1) /\ q is finite Element of K19(NAT)
D is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
E is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
len L is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
px is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
L . D is set
x9 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal set
L . E is set
(Sgm Y) . D is set
(Sgm (dom (a1 | (q \/ {q})))) . ((Sgm Y) . D) is set
(Sgm Y) . E is set
(Sgm (dom (a1 | (q \/ {q})))) . ((Sgm Y) . E) is set
len (Sgm Y) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
p9 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
(Sgm Y) . p9 is set
f39 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
(Sgm Y) . f39 is set
f49 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
q2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
(dom a1) \ q is finite Element of K19(NAT)
rng a1 is finite set
a1 . q is set
a1 /. q is Element of the carrier of K
px is Element of the carrier of K
<*px*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
dom <*px*> is non empty V12() finite 1 -element Element of K19(NAT)
<*q*> is Relation-like NAT -defined NAT -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on NAT
1 -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
rng <*q*> is non empty V12() finite 1 -element set
dom <*q*> is non empty V12() finite 1 -element Element of K19(NAT)
a1 * <*q*> is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
dom (a1 * <*q*>) is finite set
x9 is set
(a1 * <*q*>) . x9 is set
<*q*> . x9 is set
a1 . (<*q*> . x9) is set
<*px*> . x9 is set
D is non empty set
E is non empty set
K20(D,E) is Relation-like set
K19(K20(D,E)) is cup-closed diff-closed preBoolean set
pp is Relation-like NAT -defined Function-like FinSubsequence-like set
dom pp is set
Sgm (dom pp) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom pp)) is finite set
rng ((Sgm (dom (a1 | (q \/ {q})))) |-- q) is finite set
rng ((Sgm (dom (a1 | (q \/ {q})))) -| q) is finite set
a1 * (Sgm (dom (a1 | (q \/ {q})))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
{.q.} is non empty V12() finite V47() 1 -element Element of Fin NAT
q \/ {.q.} is non empty finite Element of Fin NAT
p . (q \/ {.q.}) is Element of the carrier of K
q2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q2 is Element of the carrier of K
f39 is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of D
p9 is Relation-like Function-like non empty total V18(D,E) Element of K19(K20(D,E))
p9 * f39 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
f49 is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of D
p9 * f49 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p3 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
rng p3 is finite set
p4 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
rng p4 is finite set
Sgm (dom (a1 | q)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom (a1 | q))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
p . q is Element of the carrier of K
q1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q1 is Element of the carrier of K
(Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}) is finite Element of K19(NAT)
(Sgm (dom (a1 | (q \/ {q})))) | ((Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q})) is Relation-like NAT -defined (Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}) -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT,NAT))
rng ((Sgm (dom (a1 | (q \/ {q})))) | ((Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}))) is finite set
(Sgm (dom (a1 | (q \/ {q})))) .: ((Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q})) is finite set
(dom (Sgm (dom (a1 | (q \/ {q}))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}) is finite Element of K19(NAT)
(Sgm (dom (a1 | (q \/ {q})))) .: ((dom (Sgm (dom (a1 | (q \/ {q}))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q})) is finite set
(Sgm (dom (a1 | (q \/ {q})))) .: (dom (Sgm (dom (a1 | (q \/ {q}))))) is finite set
((Sgm (dom (a1 | (q \/ {q})))) .: (dom (Sgm (dom (a1 | (q \/ {q})))))) \ {q} is finite Element of K19(((Sgm (dom (a1 | (q \/ {q})))) .: (dom (Sgm (dom (a1 | (q \/ {q})))))))
K19(((Sgm (dom (a1 | (q \/ {q})))) .: (dom (Sgm (dom (a1 | (q \/ {q}))))))) is cup-closed diff-closed preBoolean finite V47() set
pB9x is Relation-like NAT -defined Function-like FinSubsequence-like set
dom pB9x is set
Sgm (dom pB9x) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom pB9x)) is finite set
(rng (Sgm (dom pB9x))) \ {q} is finite Element of K19((rng (Sgm (dom pB9x))))
K19((rng (Sgm (dom pB9x)))) is cup-closed diff-closed preBoolean finite V47() set
(dom (a1 | (q \/ {q}))) \ {q} is finite Element of K19((dom (a1 | (q \/ {q}))))
K19((dom (a1 | (q \/ {q})))) is cup-closed diff-closed preBoolean finite V47() set
((dom a1) /\ (q \/ {q})) \ {q} is finite Element of K19(NAT)
(dom a1) /\ {q} is finite Element of K19(NAT)
((dom a1) /\ q) \/ ((dom a1) /\ {q}) is finite Element of K19(NAT)
(((dom a1) /\ q) \/ ((dom a1) /\ {q})) \ {q} is finite Element of K19(NAT)
((dom a1) /\ q) \/ {q} is non empty finite set
(((dom a1) /\ q) \/ {q}) \ {q} is finite Element of K19((((dom a1) /\ q) \/ {q}))
K19((((dom a1) /\ q) \/ {q})) is cup-closed diff-closed preBoolean finite V47() set
(dom (a1 | q)) \ {q} is finite Element of K19((dom (a1 | q)))
K19((dom (a1 | q))) is cup-closed diff-closed preBoolean finite V47() set
Sgm ((Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom (a1 | (q \/ {q})))) * (Sgm ((Seg (len (Sgm (dom (a1 | (q \/ {q})))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}))) is Relation-like NAT -defined NAT -valued Function-like finite Element of K19(K20(NAT,NAT))
Sgm ((dom (Sgm (dom (a1 | (q \/ {q}))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom (a1 | (q \/ {q})))) * (Sgm ((dom (Sgm (dom (a1 | (q \/ {q}))))) \ ((Sgm (dom (a1 | (q \/ {q})))) " {q}))) is Relation-like NAT -defined NAT -valued Function-like finite Element of K19(K20(NAT,NAT))
(Sgm (dom (a1 | (q \/ {q})))) - {q} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
((Sgm (dom (a1 | (q \/ {q})))) -| q) ^ ((Sgm (dom (a1 | (q \/ {q})))) |-- q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p3 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
p4 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
p3 ^ p4 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
x9 is Element of D
<*x9*> is Relation-like NAT -defined D -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on D
1 -tuples_on D is functional non empty FinSequence-membered FinSequenceSet of D
f39 ^ <*x9*> is Relation-like NAT -defined D -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of D
(f39 ^ <*x9*>) ^ f49 is Relation-like NAT -defined D -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of D
p9 * ((f39 ^ <*x9*>) ^ f49) is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p9 * (f39 ^ <*x9*>) is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
(p9 * (f39 ^ <*x9*>)) ^ (p9 * f49) is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p9 * <*x9*> is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
(p9 * f39) ^ (p9 * <*x9*>) is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
((p9 * f39) ^ (p9 * <*x9*>)) ^ (p9 * f49) is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p3 ^ <*px*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(p3 ^ <*px*>) ^ p4 is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
p . (q \/ {q}) is set
Sum (p3 ^ <*px*>) is Element of the carrier of K
Sum p4 is Element of the carrier of K
(Sum (p3 ^ <*px*>)) + (Sum p4) is Element of the carrier of K
the addF of K . ((Sum (p3 ^ <*px*>)),(Sum p4)) is Element of the carrier of K
Sum p3 is Element of the carrier of K
Sum <*px*> is Element of the carrier of K
(Sum p3) + (Sum <*px*>) is Element of the carrier of K
the addF of K . ((Sum p3),(Sum <*px*>)) is Element of the carrier of K
((Sum p3) + (Sum <*px*>)) + (Sum p4) is Element of the carrier of K
the addF of K . (((Sum p3) + (Sum <*px*>)),(Sum p4)) is Element of the carrier of K
(Sum p3) + (Sum p4) is Element of the carrier of K
the addF of K . ((Sum p3),(Sum p4)) is Element of the carrier of K
((Sum p3) + (Sum p4)) + (Sum <*px*>) is Element of the carrier of K
the addF of K . (((Sum p3) + (Sum p4)),(Sum <*px*>)) is Element of the carrier of K
(Sum q1) + (Sum <*px*>) is Element of the carrier of K
the addF of K . ((Sum q1),(Sum <*px*>)) is Element of the carrier of K
the addF of K . ((Sum q1),px) is Element of the carrier of K
the_unity_wrt the addF of K is Element of the carrier of K
[#] (a1,(the_unity_wrt the addF of K)) is Relation-like Function-like non empty total V18( NAT , the carrier of K) Element of K19(K20(NAT, the carrier of K))
([#] (a1,(the_unity_wrt the addF of K))) . q is Element of the carrier of K
the addF of K . ((p . q),(([#] (a1,(the_unity_wrt the addF of K))) . q)) is Element of the carrier of K
q is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
{q} is non empty V12() finite V47() 1 -element set
a1 | {q} is Relation-like NAT -defined {q} -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | {q}) is finite set
Sgm (dom (a1 | {q})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom (a1 | {q}))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
{.q.} is non empty V12() finite V47() 1 -element Element of Fin NAT
p . {.q.} is Element of the carrier of K
q is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q is Element of the carrier of K
Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K19(NAT)
(dom a1) /\ {q} is finite Element of K19(NAT)
Sgm {} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm {}) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
{} * a1 is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered set
p . {q} is set
0. K is V63(K) Element of the carrier of K
([#] (a1,(the_unity_wrt the addF of K))) . q is Element of the carrier of K
a1 . q is set
a1 /. q is Element of the carrier of K
px is Element of the carrier of K
<*px*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
dom <*px*> is non empty V12() finite 1 -element Element of K19(NAT)
<*q*> is Relation-like NAT -defined NAT -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on NAT
rng <*q*> is non empty V12() finite 1 -element set
dom <*q*> is non empty V12() finite 1 -element Element of K19(NAT)
a1 * <*q*> is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
dom (a1 * <*q*>) is finite set
e is set
(a1 * <*q*>) . e is set
<*q*> . e is set
a1 . (<*q*> . e) is set
<*px*> . e is set
(dom a1) /\ {q} is finite Element of K19(NAT)
Sgm ((dom a1) /\ {q}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm ((dom a1) /\ {q})) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
Sgm {q} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm {q}) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
p . {q} is set
([#] (a1,(the_unity_wrt the addF of K))) . q is Element of the carrier of K
q is Element of the carrier of K
0. K is V63(K) Element of the carrier of K
{}. NAT is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of Fin NAT
a1 | ({}. NAT) is Relation-like non-empty empty-yielding NAT -defined {}. NAT -defined NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K19(K20(NAT, the carrier of K))
dom (a1 | ({}. NAT)) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K19(NAT)
Sgm (dom (a1 | ({}. NAT))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom (a1 | ({}. NAT)))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
p . ({}. NAT) is Element of the carrier of K
q is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q is Element of the carrier of K
dom {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K19(NAT)
Sgm (dom {}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom {})) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
{} * a1 is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered set
p . {} is set
a1 | (dom a1) is Relation-like NAT -defined dom a1 -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | (dom a1)) is finite set
Sgm (dom (a1 | (dom a1))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom (a1 | (dom a1)))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
findom a1 is finite Element of Fin NAT
p . (findom a1) is Element of the carrier of K
q is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum q is Element of the carrier of K
Sgm (dom a1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (dom a1)) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
Sgm (Seg (len a1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
a1 * (Sgm (Seg (len a1))) is Relation-like NAT -defined the carrier of K -valued Function-like finite Element of K19(K20(NAT, the carrier of K))
idseq (len a1) is Relation-like NAT -defined Function-like finite len a1 -element FinSequence-like FinSubsequence-like set
(idseq (len a1)) * a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite set
the addF of K $$ ((findom a1),([#] (a1,(the_unity_wrt the addF of K)))) is Element of the carrier of K
a1 | (len a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 | (Seg (len a1)) is Relation-like NAT -defined Seg (len a1) -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
p is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
q is Element of the carrier of K
p + 1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
a1 . (p + 1) is set
a1 | (p + 1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (a1 | (p + 1)) is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg p is finite p -element Element of K19(NAT)
Seg (p + 1) is non empty finite p + 1 -element Element of K19(NAT)
a1 | p is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a1 | (Seg p) is Relation-like NAT -defined Seg p -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
a1 | (Seg (p + 1)) is Relation-like NAT -defined Seg (p + 1) -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
(a1 | (Seg (p + 1))) | (Seg p) is Relation-like NAT -defined Seg p -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
(a1 | (p + 1)) | (Seg p) is Relation-like NAT -defined Seg p -defined NAT -defined the carrier of K -valued Function-like finite FinSubsequence-like Element of K19(K20(NAT, the carrier of K))
dom (a1 | (p + 1)) is finite Element of K19(NAT)
a1 /. (p + 1) is Element of the carrier of K
(a1 | (p + 1)) /. (p + 1) is Element of the carrier of K
(a1 | (p + 1)) . (p + 1) is set
<*q*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(a1 | p) ^ <*q*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
b2 . (p + 1) is Element of the carrier of K
the addF of K "**" ((a1 | p) ^ <*q*>) is Element of the carrier of K
the addF of K "**" (a1 | p) is Element of the carrier of K
the addF of K . (( the addF of K "**" (a1 | p)),q) is Element of the carrier of K
b2 . p is Element of the carrier of K
(b2 . p) + q is Element of the carrier of K
the addF of K . ((b2 . p),q) is Element of the carrier of K
a1 | 0 is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
b2 . 0 is Element of the carrier of K
the addF of K "**" (<*> the carrier of K) is Element of the carrier of K
b2 . (len a1) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 ^ <*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (a2 ^ <*a1*>) is Element of the carrier of K
Sum a2 is Element of the carrier of K
(Sum a2) + a1 is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K . ((Sum a2),a1) is Element of the carrier of K
Sum <*a1*> is Element of the carrier of K
(Sum a2) + (Sum <*a1*>) is Element of the carrier of K
the addF of K . ((Sum a2),(Sum <*a1*>)) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like add-associative right_zeroed addLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*a1*> ^ a2 is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (<*a1*> ^ a2) is Element of the carrier of K
Sum a2 is Element of the carrier of K
a1 + (Sum a2) is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K . (a1,(Sum a2)) is Element of the carrier of K
Sum <*a1*> is Element of the carrier of K
(Sum <*a1*>) + (Sum a2) is Element of the carrier of K
the addF of K . ((Sum <*a1*>),(Sum a2)) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed right-distributive left-distributive distributive doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a2,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
the multF of K [;] (a1,(id the carrier of K)) is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
(K,a1) * a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,a2,a1) is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
the addF of K "**" (K,a2,a1) is Element of the carrier of K
Sum a2 is Element of the carrier of K
the addF of K "**" a2 is Element of the carrier of K
a1 * (Sum a2) is Element of the carrier of K
the multF of K . (a1,(Sum a2)) is Element of the carrier of K
( the multF of K [;] (a1,(id the carrier of K))) . (Sum a2) is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
0 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V63(K) Element of the carrier of K
a1 is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on the carrier of K
Sum a1 is Element of the carrier of K
<*> the carrier of K is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
comp K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K19(K20( the carrier of K, the carrier of K)) is cup-closed diff-closed preBoolean set
(comp K) * a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,a1) is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the addF of K "**" (K,a1) is Element of the carrier of K
Sum a1 is Element of the carrier of K
the addF of K "**" a1 is Element of the carrier of K
- (Sum a1) is Element of the carrier of K
the_inverseOp_wrt the addF of K is Relation-like Function-like non empty total V18( the carrier of K, the carrier of K) Element of K19(K20( the carrier of K, the carrier of K))
(comp K) . (Sum a1) is Element of the carrier of K
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
Sum (K,a1,a2,b1) is Element of the carrier of a1
the addF of a1 "**" (K,a1,a2,b1) is Element of the carrier of a1
Sum a2 is Element of the carrier of a1
the addF of a1 "**" a2 is Element of the carrier of a1
Sum b1 is Element of the carrier of a1
the addF of a1 "**" b1 is Element of the carrier of a1
(Sum a2) + (Sum b1) is Element of the carrier of a1
the addF of a1 . ((Sum a2),(Sum b1)) is Element of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed addLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
Sum a2 is Element of the carrier of a1
the addF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the addF of a1 "**" a2 is Element of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
comp a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the addF of a1 * ((id the carrier of a1),(comp a1)) is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
(a1) .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
Sum (K,a1,a2,b1) is Element of the carrier of a1
the addF of a1 "**" (K,a1,a2,b1) is Element of the carrier of a1
Sum b1 is Element of the carrier of a1
the addF of a1 "**" b1 is Element of the carrier of a1
(Sum a2) - (Sum b1) is Element of the carrier of a1
- (Sum b1) is Element of the carrier of a1
(Sum a2) + (- (Sum b1)) is Element of the carrier of a1
the addF of a1 . ((Sum a2),(- (Sum b1))) is Element of the carrier of a1
the_inverseOp_wrt the addF of a1 is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1) . ((Sum a2),( the addF of a1 "**" b1)) is Element of the carrier of a1
K is non empty unital commutative right_unital well-unital left_unital multLoopStr
the carrier of K is non empty set
<*> the carrier of K is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
Product (<*> the carrier of K) is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K "**" (<*> the carrier of K) is Element of the carrier of K
1. K is Element of the carrier of K
1_ K is Element of the carrier of K
K is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*a1*> ^ a2 is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Product (<*a1*> ^ a2) is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K "**" (<*a1*> ^ a2) is Element of the carrier of K
Product a2 is Element of the carrier of K
the multF of K "**" a2 is Element of the carrier of K
a1 * (Product a2) is Element of the carrier of K
the multF of K . (a1,(Product a2)) is Element of the carrier of K
Product <*a1*> is Element of the carrier of K
the multF of K "**" <*a1*> is Element of the carrier of K
(Product <*a1*>) * (Product a2) is Element of the carrier of K
the multF of K . ((Product <*a1*>),(Product a2)) is Element of the carrier of K
K is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K . (a1,a2) is Element of the carrier of K
b1 is Element of the carrier of K
<*a1,a2,b1*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Product <*a1,a2,b1*> is Element of the carrier of K
the multF of K "**" <*a1,a2,b1*> is Element of the carrier of K
(a1 * a2) * b1 is Element of the carrier of K
the multF of K . ((a1 * a2),b1) is Element of the carrier of K
<*a1,a2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
<*b1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
<*a1,a2*> ^ <*b1*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 + 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
2 + 1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
Product (<*a1,a2*> ^ <*b1*>) is Element of the carrier of K
the multF of K "**" (<*a1,a2*> ^ <*b1*>) is Element of the carrier of K
Product <*a1,a2*> is Element of the carrier of K
the multF of K "**" <*a1,a2*> is Element of the carrier of K
(Product <*a1,a2*>) * b1 is Element of the carrier of K
the multF of K . ((Product <*a1,a2*>),b1) is Element of the carrier of K
K is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of K is non empty set
0 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is Element of the carrier of K
a1 is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on the carrier of K
Product a1 is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K "**" a1 is Element of the carrier of K
<*> the carrier of K is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a1 is non empty set
1_ a1 is Element of the carrier of a1
1. a1 is Element of the carrier of a1
K |-> (1_ a1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
Product (K |-> (1_ a1)) is Element of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 "**" (K |-> (1_ a1)) is Element of the carrier of a1
the_unity_wrt the multF of a1 is Element of the carrier of a1
K is non empty non degenerated V61() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible left_zeroed add-left-invertible add-right-invertible Loop-like unital associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty V12() set
0. K is V63(K) Element of the carrier of K
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
dom a1 is finite Element of K19(NAT)
Product a1 is Element of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K "**" a1 is Element of the carrier of K
a2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg a2 is finite a2 -element Element of K19(NAT)
a2 + 1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
Seg (a2 + 1) is non empty finite a2 + 1 -element Element of K19(NAT)
b1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len b1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Product b1 is Element of the carrier of K
the multF of K "**" b1 is Element of the carrier of K
b2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
p is Element of the carrier of K
<*p*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
b2 ^ <*p*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len b2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
(len b2) + 1 is non empty V29() V30() V31() V35() V36() ext-real positive non negative V40() finite cardinal Element of NAT
Product b2 is Element of the carrier of K
the multF of K "**" b2 is Element of the carrier of K
(Product b2) * p is Element of the carrier of K
the multF of K . ((Product b2),p) is Element of the carrier of K
q is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
b1 . q is set
dom b2 is finite Element of K19(NAT)
b2 . q is set
q is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
b2 . q is set
dom b2 is finite Element of K19(NAT)
b1 . q is set
b1 . (a2 + 1) is set
len a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Seg (len a1) is finite len a1 -element Element of K19(NAT)
Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K19(NAT)
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len a2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
Product a2 is Element of the carrier of K
the multF of K "**" a2 is Element of the carrier of K
<*> the carrier of K is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like one-to-one constant functional empty V29() V30() V31() V33() V34() V35() V36() ext-real non negative V40() finite finite-yielding V47() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of K
1. K is V63(K) Element of the carrier of K
b1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a2 . b1 is set
a2 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 . a2 is set
a2 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a2 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K + a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
b1 is Element of the carrier of a2
(K + a1) |-> b1 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K + a1 -element FinSequence-like FinSubsequence-like Element of (K + a1) -tuples_on the carrier of a2
(K + a1) -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product ((K + a1) |-> b1) is Element of the carrier of a2
the multF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the multF of a2 "**" ((K + a1) |-> b1) is Element of the carrier of a2
K |-> b1 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a2
K -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product (K |-> b1) is Element of the carrier of a2
the multF of a2 "**" (K |-> b1) is Element of the carrier of a2
a1 |-> b1 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product (a1 |-> b1) is Element of the carrier of a2
the multF of a2 "**" (a1 |-> b1) is Element of the carrier of a2
(Product (K |-> b1)) * (Product (a1 |-> b1)) is Element of the carrier of a2
the multF of a2 . ((Product (K |-> b1)),(Product (a1 |-> b1))) is Element of the carrier of a2
a2 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a2 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K * a1 is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
b1 is Element of the carrier of a2
(K * a1) |-> b1 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K * a1 -element FinSequence-like FinSubsequence-like Element of (K * a1) -tuples_on the carrier of a2
(K * a1) -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product ((K * a1) |-> b1) is Element of the carrier of a2
the multF of a2 is Relation-like Function-like total V18(K20( the carrier of a2, the carrier of a2), the carrier of a2) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2))
K20( the carrier of a2, the carrier of a2) is Relation-like set
K20(K20( the carrier of a2, the carrier of a2), the carrier of a2) is Relation-like set
K19(K20(K20( the carrier of a2, the carrier of a2), the carrier of a2)) is cup-closed diff-closed preBoolean set
the multF of a2 "**" ((K * a1) |-> b1) is Element of the carrier of a2
K |-> b1 is Relation-like NAT -defined the carrier of a2 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a2
K -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product (K |-> b1) is Element of the carrier of a2
the multF of a2 "**" (K |-> b1) is Element of the carrier of a2
a1 |-> (Product (K |-> b1)) is Relation-like NAT -defined the carrier of a2 -valued Function-like finite a1 -element FinSequence-like FinSubsequence-like Element of a1 -tuples_on the carrier of a2
a1 -tuples_on the carrier of a2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a2
Product (a1 |-> (Product (K |-> b1))) is Element of the carrier of a2
the multF of a2 "**" (a1 |-> (Product (K |-> b1))) is Element of the carrier of a2
a1 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a2 is Element of the carrier of a1
b1 is Element of the carrier of a1
a2 * b1 is Element of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 . (a2,b1) is Element of the carrier of a1
K |-> (a2 * b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
Product (K |-> (a2 * b1)) is Element of the carrier of a1
the multF of a1 "**" (K |-> (a2 * b1)) is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
Product (K |-> a2) is Element of the carrier of a1
the multF of a1 "**" (K |-> a2) is Element of the carrier of a1
K |-> b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
Product (K |-> b1) is Element of the carrier of a1
the multF of a1 "**" (K |-> b1) is Element of the carrier of a1
(Product (K |-> a2)) * (Product (K |-> b1)) is Element of the carrier of a1
the multF of a1 . ((Product (K |-> a2)),(Product (K |-> b1))) is Element of the carrier of a1
a1 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a1 is non empty set
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 .: (a2,b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
Product (K,a1,a2,b1) is Element of the carrier of a1
the multF of a1 "**" (K,a1,a2,b1) is Element of the carrier of a1
Product a2 is Element of the carrier of a1
the multF of a1 "**" a2 is Element of the carrier of a1
Product b1 is Element of the carrier of a1
the multF of a1 "**" b1 is Element of the carrier of a1
(Product a2) * (Product b1) is Element of the carrier of a1
the multF of a1 . ((Product a2),(Product b1)) is Element of the carrier of a1
K is V29() V30() V31() V35() V36() ext-real non negative V40() finite cardinal Element of NAT
a1 is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of a1 is non empty set
K -tuples_on the carrier of a1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of a1
a2 is Element of the carrier of a1
K |-> a2 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
Product (K |-> a2) is Element of the carrier of a1
the multF of a1 is Relation-like Function-like total V18(K20( the carrier of a1, the carrier of a1), the carrier of a1) commutative associative having_a_unity Element of K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1))
K20( the carrier of a1, the carrier of a1) is Relation-like set
K20(K20( the carrier of a1, the carrier of a1), the carrier of a1) is Relation-like set
K19(K20(K20( the carrier of a1, the carrier of a1), the carrier of a1)) is cup-closed diff-closed preBoolean set
the multF of a1 "**" (K |-> a2) is Element of the carrier of a1
b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(K,a1,b1,a2) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
(a1,a2) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
K19(K20( the carrier of a1, the carrier of a1)) is cup-closed diff-closed preBoolean set
id the carrier of a1 is Relation-like the carrier of a1 -defined the carrier of a1 -valued Function-like one-to-one non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
the multF of a1 [;] (a2,(id the carrier of a1)) is Relation-like Function-like non empty total V18( the carrier of a1, the carrier of a1) Element of K19(K20( the carrier of a1, the carrier of a1))
(a1,a2) * b1 is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
Product (K,a1,b1,a2) is Element of the carrier of a1
the multF of a1 "**" (K,a1,b1,a2) is Element of the carrier of a1
Product b1 is Element of the carrier of a1
the multF of a1 "**" b1 is Element of the carrier of a1
(Product (K |-> a2)) * (Product b1) is Element of the carrier of a1
the multF of a1 . ((Product (K |-> a2)),(Product b1)) is Element of the carrier of a1
(K,a1,(K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of a1
the multF of a1 .: ((K |-> a2),b1) is Relation-like NAT -defined the carrier of a1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of a1
Product (K,a1,(K |-> a2),b1) is Element of the carrier of a1
the multF of a1 "**" (K,a1,(K |-> a2),b1) is Element of the carrier of a1
K is non empty doubleLoopStr
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,a1,a2) is Element of the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like unital associative commutative Abelian add-associative right_zeroed right_unital left_unital doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
<*a1*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
a2 is Element of the carrier of K
<*a2*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
(K,<*a1*>,<*a2*>) is Element of the carrier of K
(K,<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,<*a1*>,<*a2*>) is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
the addF of K "**" (K,<*a1*>,<*a2*>) is Element of the carrier of K
a1 * a2 is Element of the carrier of K
the multF of K . (a1,a2) is Element of the carrier of K
(1,K,<*a1*>,<*a2*>) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
<*(a1 * a2)*> is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
1 |-> (a1 * a2) is Relation-like NAT -defined the carrier of K -valued Function-like constant non empty V12() finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of K
K is non empty left_add-cancelable right_add-cancelable right_complementable left_zeroed add-left-invertible add-right-invertible Loop-like unital associative commutative Abelian add-associative right_zeroed right_unital left_unital doubleLoopStr
the carrier of K is non empty set
a1 is Element of the carrier of K
a2 is Element of the carrier of K
<*a1,a2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
b1 is Element of the carrier of K
b2 is Element of the carrier of K
<*b1,b2*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,<*a1,a2*>,<*b1,b2*>) is Element of the carrier of K
(K,<*a1,a2*>,<*b1,b2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (<*a1,a2*>,<*b1,b2*>) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,<*a1,a2*>,<*b1,b2*>) is Element of the carrier of K
the addF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
the addF of K "**" (K,<*a1,a2*>,<*b1,b2*>) is Element of the carrier of K
a1 * b1 is Element of the carrier of K
the multF of K . (a1,b1) is Element of the carrier of K
a2 * b2 is Element of the carrier of K
the multF of K . (a2,b2) is Element of the carrier of K
(a1 * b1) + (a2 * b2) is Element of the carrier of K
the addF of K . ((a1 * b1),(a2 * b2)) is Element of the carrier of K
<*(a1 * b1),(a2 * b2)*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the addF of K "**" <*(a1 * b1),(a2 * b2)*> is Element of the carrier of K
K is non empty unital associative commutative right_unital well-unital left_unital doubleLoopStr
the carrier of K is non empty set
a1 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
a2 is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,a1,a2) is Element of the carrier of K
(K,a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K is Relation-like Function-like total V18(K20( the carrier of K, the carrier of K), the carrier of K) commutative associative having_a_unity Element of K19(K20(K20( the carrier of K, the carrier of K), the carrier of K))
K20( the carrier of K, the carrier of K) is Relation-like set
K20(K20( the carrier of K, the carrier of K), the carrier of K) is Relation-like set
K19(K20(K20( the carrier of K, the carrier of K), the carrier of K)) is cup-closed diff-closed preBoolean set
the multF of K .: (a1,a2) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,a1,a2) is Element of the carrier of K
(K,a2,a1) is Element of the carrier of K
(K,a2,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
the multF of K .: (a2,a1) is Relation-like NAT -defined the carrier of K -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Sum (K,a2,a1) is Element of the carrier of K