:: GROUP_3 semantic presentation

K109() is set
K113() is non empty V12() V13() V14() Element of bool K109()
bool K109() is non empty set
K110() is set
K46() is non empty V12() V13() V14() set
bool K46() is non empty set
K111() is set
K112() is set
[:K110(),K110():] is set
bool [:K110(),K110():] is non empty set
[:[:K110(),K110():],K110():] is set
bool [:[:K110(),K110():],K110():] is non empty set
[:K109(),K109():] is set
bool [:K109(),K109():] is non empty set
[:[:K109(),K109():],K109():] is set
bool [:[:K109(),K109():],K109():] is non empty set
[:K111(),K111():] is set
bool [:K111(),K111():] is non empty set
[:[:K111(),K111():],K111():] is set
bool [:[:K111(),K111():],K111():] is non empty set
[:K112(),K112():] is set
bool [:K112(),K112():] is non empty set
[:[:K112(),K112():],K112():] is set
bool [:[:K112(),K112():],K112():] is non empty set
[:K113(),K113():] is non empty set
[:[:K113(),K113():],K113():] is non empty set
bool [:[:K113(),K113():],K113():] is non empty set

the empty V12() V13() V14() V16() V17() V18() Function-like functional ext-real V37() V38() integer finite V45() set is empty V12() V13() V14() V16() V17() V18() Function-like functional ext-real V37() V38() integer finite V45() set
1 is non empty V12() V13() V14() V18() ext-real V37() V38() integer Element of K113()
K114() is empty V12() V13() V14() V16() V17() V18() Function-like functional ext-real V37() V38() integer finite V45() Element of K113()
2 is non empty V12() V13() V14() V18() ext-real V37() V38() integer Element of K113()

the carrier of G is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
H * a is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
a " is Element of the carrier of G
(H * a) * (a ") is Element of the carrier of G
the multF of G . ((H * a),(a ")) is Element of the carrier of G
[(H * a),(a ")] is set
{(H * a),(a ")} is non empty finite set
{(H * a)} is non empty finite set
{{(H * a),(a ")},{(H * a)}} is non empty finite V45() set
the multF of G . [(H * a),(a ")] is set
H * (a ") is Element of the carrier of G
the multF of G . (H,(a ")) is Element of the carrier of G
[H,(a ")] is set
{H,(a ")} is non empty finite set
{{H,(a ")},{H}} is non empty finite V45() set
the multF of G . [H,(a ")] is set
(H * (a ")) * a is Element of the carrier of G
the multF of G . ((H * (a ")),a) is Element of the carrier of G
[(H * (a ")),a] is set
{(H * (a ")),a} is non empty finite set
{(H * (a "))} is non empty finite set
{{(H * (a ")),a},{(H * (a "))}} is non empty finite V45() set
the multF of G . [(H * (a ")),a] is set
(a ") * a is Element of the carrier of G
the multF of G . ((a "),a) is Element of the carrier of G
[(a "),a] is set
{(a "),a} is non empty finite set
{(a ")} is non empty finite set
{{(a "),a},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),a] is set
((a ") * a) * H is Element of the carrier of G
the multF of G . (((a ") * a),H) is Element of the carrier of G
[((a ") * a),H] is set
{((a ") * a),H} is non empty finite set
{((a ") * a)} is non empty finite set
{{((a ") * a),H},{((a ") * a)}} is non empty finite V45() set
the multF of G . [((a ") * a),H] is set
a * (a ") is Element of the carrier of G
the multF of G . (a,(a ")) is Element of the carrier of G
[a,(a ")] is set
{a,(a ")} is non empty finite set
{a} is non empty finite set
{{a,(a ")},{a}} is non empty finite V45() set
the multF of G . [a,(a ")] is set
(a * (a ")) * H is Element of the carrier of G
the multF of G . ((a * (a ")),H) is Element of the carrier of G
[(a * (a ")),H] is set
{(a * (a ")),H} is non empty finite set
{(a * (a "))} is non empty finite set
{{(a * (a ")),H},{(a * (a "))}} is non empty finite V45() set
the multF of G . [(a * (a ")),H] is set
H * (a * (a ")) is Element of the carrier of G
the multF of G . (H,(a * (a "))) is Element of the carrier of G
[H,(a * (a "))] is set
{H,(a * (a "))} is non empty finite set
{{H,(a * (a "))},{H}} is non empty finite V45() set
the multF of G . [H,(a * (a "))] is set
H * ((a ") * a) is Element of the carrier of G
the multF of G . (H,((a ") * a)) is Element of the carrier of G
[H,((a ") * a)] is set
{H,((a ") * a)} is non empty finite set
{{H,((a ") * a)},{H}} is non empty finite V45() set
the multF of G . [H,((a ") * a)] is set
a * H is Element of the carrier of G
the multF of G . (a,H) is Element of the carrier of G
[a,H] is set
{a,H} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of G . [a,H] is set
(a ") * (a * H) is Element of the carrier of G
the multF of G . ((a "),(a * H)) is Element of the carrier of G
[(a "),(a * H)] is set
{(a "),(a * H)} is non empty finite set
{{(a "),(a * H)},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),(a * H)] is set
(a ") * H is Element of the carrier of G
the multF of G . ((a "),H) is Element of the carrier of G
[(a "),H] is set
{(a "),H} is non empty finite set
{{(a "),H},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),H] is set
a * ((a ") * H) is Element of the carrier of G
the multF of G . (a,((a ") * H)) is Element of the carrier of G
[a,((a ") * H)] is set
{a,((a ") * H)} is non empty finite set
{{a,((a ") * H)},{a}} is non empty finite V45() set
the multF of G . [a,((a ") * H)] is set
1_ G is non being_of_order_0 Element of the carrier of G
H * (1_ G) is Element of the carrier of G
the multF of G . (H,(1_ G)) is Element of the carrier of G
[H,(1_ G)] is set
{H,(1_ G)} is non empty finite set
{{H,(1_ G)},{H}} is non empty finite V45() set
the multF of G . [H,(1_ G)] is set
(1_ G) * H is Element of the carrier of G
the multF of G . ((1_ G),H) is Element of the carrier of G
[(1_ G),H] is set
{(1_ G),H} is non empty finite set
{(1_ G)} is non empty finite set
{{(1_ G),H},{(1_ G)}} is non empty finite V45() set
the multF of G . [(1_ G),H] is set

the carrier of G is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
H * a is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
a * H is Element of the carrier of G
the multF of G . (a,H) is Element of the carrier of G
[a,H] is set
{a,H} is non empty finite set
{a} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of G . [a,H] is set

the carrier of G is non empty set
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
the multF of G . (a,H) is Element of the carrier of G
[a,H] is set
{a,H} is non empty finite set
{a} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of G . [a,H] is set
the multF of G . (H,a) is Element of the carrier of G
H * a is Element of the carrier of G
a * H is Element of the carrier of G
the multF of G . (a,H) is Element of the carrier of G
H is Element of the carrier of G
a is Element of the carrier of G
H * a is Element of the carrier of G
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
a * H is Element of the carrier of G
the multF of G . (a,H) is Element of the carrier of G
[a,H] is set
{a,H} is non empty finite set
{a} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of G . [a,H] is set

the carrier of ((1). G) is non empty finite set
H is Element of the carrier of ((1). G)
a is Element of the carrier of ((1). G)
H * a is Element of the carrier of ((1). G)
the multF of ((1). G) is Relation-like [: the carrier of ((1). G), the carrier of ((1). G):] -defined the carrier of ((1). G) -valued Function-like V28([: the carrier of ((1). G), the carrier of ((1). G):], the carrier of ((1). G)) associative finite Element of bool [:[: the carrier of ((1). G), the carrier of ((1). G):], the carrier of ((1). G):]
[: the carrier of ((1). G), the carrier of ((1). G):] is non empty finite set
[:[: the carrier of ((1). G), the carrier of ((1). G):], the carrier of ((1). G):] is non empty finite set
bool [:[: the carrier of ((1). G), the carrier of ((1). G):], the carrier of ((1). G):] is non empty finite V45() set
the multF of ((1). G) . (H,a) is Element of the carrier of ((1). G)
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of ((1). G) . [H,a] is set
a * H is Element of the carrier of ((1). G)
the multF of ((1). G) . (a,H) is Element of the carrier of ((1). G)
[a,H] is set
{a,H} is non empty finite set
{a} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of ((1). G) . [a,H] is set
the carrier of G is non empty set
1_ G is non being_of_order_0 Element of the carrier of G
{(1_ G)} is non empty finite Element of bool the carrier of G
bool the carrier of G is non empty set

the carrier of G is non empty set
bool the carrier of G is non empty set
H is Element of bool the carrier of G
a is Element of bool the carrier of G
c4 is Element of bool the carrier of G
H * c4 is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in H & b2 in c4 ) } is set
y is Element of bool the carrier of G
a * y is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in y ) } is set
H1 is set
a is Element of the carrier of G
b is Element of the carrier of G
a * b is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (a,b) is Element of the carrier of G
[a,b] is set
{a,b} is non empty finite set
{a} is non empty finite set
{{a,b},{a}} is non empty finite V45() set
the multF of G . [a,b] is set

the carrier of G is non empty set
bool the carrier of G is non empty set
a is Element of bool the carrier of G
c4 is Element of bool the carrier of G
H is Element of the carrier of G
H * a is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
{H} * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in a ) } is set
H * c4 is Element of bool the carrier of G
{H} * c4 is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in c4 ) } is set
a * H is Element of bool the carrier of G
a * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in {H} ) } is set
c4 * H is Element of bool the carrier of G
c4 * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in c4 & b2 in {H} ) } is set

the carrier of G is non empty set
H is Element of the carrier of G
a is non empty unital Group-like associative Subgroup of G
H * a is Element of bool the carrier of G
bool the carrier of G is non empty set
carr a is Element of bool the carrier of G
the carrier of a is non empty set
H * (carr a) is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
{H} * (carr a) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr a ) } is set
a * H is Element of bool the carrier of G
(carr a) * H is Element of bool the carrier of G
(carr a) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr a & b2 in {H} ) } is set
c4 is non empty unital Group-like associative Subgroup of G
H * c4 is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
H * (carr c4) is Element of bool the carrier of G
{H} * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr c4 ) } is set
c4 * H is Element of bool the carrier of G
(carr c4) * H is Element of bool the carrier of G
(carr c4) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr c4 & b2 in {H} ) } is set

the carrier of G is non empty set
a is non empty unital Group-like associative Subgroup of G
H is Element of the carrier of G
H * a is Element of bool the carrier of G
bool the carrier of G is non empty set
carr a is Element of bool the carrier of G
the carrier of a is non empty set
H * (carr a) is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
{H} * (carr a) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr a ) } is set
{H} * a is Element of bool the carrier of G

the carrier of G is non empty set
a is non empty unital Group-like associative Subgroup of G
H is Element of the carrier of G
a * H is Element of bool the carrier of G
bool the carrier of G is non empty set
carr a is Element of bool the carrier of G
the carrier of a is non empty set
(carr a) * H is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
(carr a) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr a & b2 in {H} ) } is set
a * {H} is Element of bool the carrier of G

the carrier of G is non empty set
bool the carrier of G is non empty set
H is Element of the carrier of G
a is Element of bool the carrier of G
a * H is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
a * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in {H} ) } is set
c4 is non empty unital Group-like associative Subgroup of G
(a * H) * c4 is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
(a * H) * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a * H & b2 in carr c4 ) } is set
H * c4 is Element of bool the carrier of G
H * (carr c4) is Element of bool the carrier of G
{H} * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr c4 ) } is set
a * (H * c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in H * c4 ) } is set
{H} * c4 is Element of bool the carrier of G
a * ({H} * c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in {H} * c4 ) } is set

the carrier of G is non empty set
bool the carrier of G is non empty set
H is Element of the carrier of G
a is Element of bool the carrier of G
c4 is non empty unital Group-like associative Subgroup of G
H * c4 is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
H * (carr c4) is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
{H} * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr c4 ) } is set
(H * c4) * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in H * c4 & b2 in a ) } is set
c4 * a is Element of bool the carrier of G
(carr c4) * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr c4 & b2 in a ) } is set
H * (c4 * a) is Element of bool the carrier of G
{H} * (c4 * a) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in c4 * a ) } is set
{H} * c4 is Element of bool the carrier of G
({H} * c4) * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} * c4 & b2 in a ) } is set

the carrier of G is non empty set
bool the carrier of G is non empty set
H is Element of the carrier of G
a is Element of bool the carrier of G
c4 is non empty unital Group-like associative Subgroup of G
a * c4 is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
a * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in carr c4 ) } is set
(a * c4) * H is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
(a * c4) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a * c4 & b2 in {H} ) } is set
c4 * H is Element of bool the carrier of G
(carr c4) * H is Element of bool the carrier of G
(carr c4) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr c4 & b2 in {H} ) } is set
a * (c4 * H) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in c4 * H ) } is set
c4 * {H} is Element of bool the carrier of G
a * (c4 * {H}) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a & b2 in c4 * {H} ) } is set

the carrier of G is non empty set
bool the carrier of G is non empty set
H is Element of the carrier of G
a is Element of bool the carrier of G
H * a is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
{H} * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in a ) } is set
c4 is non empty unital Group-like associative Subgroup of G
c4 * H is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
(carr c4) * H is Element of bool the carrier of G
(carr c4) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr c4 & b2 in {H} ) } is set
(c4 * H) * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in c4 * H & b2 in a ) } is set
c4 * (H * a) is Element of bool the carrier of G
(carr c4) * (H * a) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr c4 & b2 in H * a ) } is set
c4 * {H} is Element of bool the carrier of G
(c4 * {H}) * a is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in c4 * {H} & b2 in a ) } is set

the carrier of G is non empty set
c4 is non empty unital Group-like associative Subgroup of G
a is non empty unital Group-like associative Subgroup of G
H is Element of the carrier of G
a * H is Element of bool the carrier of G
bool the carrier of G is non empty set
carr a is Element of bool the carrier of G
the carrier of a is non empty set
(carr a) * H is Element of bool the carrier of G
{H} is non empty finite Element of bool the carrier of G
(carr a) * {H} is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr a & b2 in {H} ) } is set
(a * H) * c4 is Element of bool the carrier of G
carr c4 is Element of bool the carrier of G
the carrier of c4 is non empty set
(a * H) * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in a * H & b2 in carr c4 ) } is set
H * c4 is Element of bool the carrier of G
H * (carr c4) is Element of bool the carrier of G
{H} * (carr c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in {H} & b2 in carr c4 ) } is set
a * (H * c4) is Element of bool the carrier of G
(carr a) * (H * c4) is Element of bool the carrier of G
{ (b1 * b2) where b1, b2 is Element of the carrier of G : ( b1 in carr a & b2 in H * c4 ) } is set

the carrier of G is non empty set
bool the carrier of G is non empty set
H is set
c4 is set
H1 is non empty strict unital Group-like associative Subgroup of G
a is set
the carrier of H1 is non empty set
y is set
a is non empty strict unital Group-like associative Subgroup of G
the carrier of a is non empty set

c4 is set
y is non empty strict unital Group-like associative Subgroup of G
the carrier of y is non empty set
H1 is set
[c4,H1] is set
{c4,H1} is non empty finite set
{c4} is non empty finite set
{{c4,H1},{c4}} is non empty finite V45() set
y is set
[c4,y] is set
{c4,y} is non empty finite set
{c4} is non empty finite set
{{c4,y},{c4}} is non empty finite V45() set
dom a is set
rng a is set
c4 is set
y is set
a . y is set
[y,c4] is set
{y,c4} is non empty finite set
{y} is non empty finite set
{{y,c4},{y}} is non empty finite V45() set
H1 is non empty strict unital Group-like associative Subgroup of G
the carrier of H1 is non empty set
y is non empty strict unital Group-like associative Subgroup of G
the carrier of y is non empty set
H1 is set
[H1,c4] is set
{H1,c4} is non empty finite set
{H1} is non empty finite set
{{H1,c4},{H1}} is non empty finite V45() set
a . H1 is set
H is set
a is set

(G) is set
the non empty strict unital Group-like associative Subgroup of G is non empty strict unital Group-like associative Subgroup of G

(G) is non empty set

(G) is non empty set
H is set
a is non empty strict unital Group-like associative Subgroup of G
the carrier of a is non empty set
c4 is set

dom H is set
rng H is set
the carrier of G is non empty set
bool the carrier of G is non empty set
a is set
c4 is set
H . c4 is set
y is non empty strict unital Group-like associative Subgroup of G
the carrier of y is non empty set
a is set
H . a is set
c4 is set
H . c4 is set
y is non empty strict unital Group-like associative Subgroup of G
the carrier of y is non empty set
H1 is non empty strict unital Group-like associative Subgroup of G
the carrier of H1 is non empty set
card (G) is cardinal set
card (bool the carrier of G) is cardinal set

the carrier of G is non empty set
a is Element of the carrier of G
a " is Element of the carrier of G
H is Element of the carrier of G
(a ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((a "),H) is Element of the carrier of G
[(a "),H] is set
{(a "),H} is non empty finite set
{(a ")} is non empty finite set
{{(a "),H},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),H] is set
((a ") * H) * a is Element of the carrier of G
the multF of G . (((a ") * H),a) is Element of the carrier of G
[((a ") * H),a] is set
{((a ") * H),a} is non empty finite set
{((a ") * H)} is non empty finite set
{{((a ") * H),a},{((a ") * H)}} is non empty finite V45() set
the multF of G . [((a ") * H),a] is set

the carrier of G is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
(G,H,a) is Element of the carrier of G
a " is Element of the carrier of G
(a ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((a "),H) is Element of the carrier of G
[(a "),H] is set
{(a "),H} is non empty finite set
{(a ")} is non empty finite set
{{(a "),H},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),H] is set
((a ") * H) * a is Element of the carrier of G
the multF of G . (((a ") * H),a) is Element of the carrier of G
[((a ") * H),a] is set
{((a ") * H),a} is non empty finite set
{((a ") * H)} is non empty finite set
{{((a ") * H),a},{((a ") * H)}} is non empty finite V45() set
the multF of G . [((a ") * H),a] is set
c4 is Element of the carrier of G
(G,c4,a) is Element of the carrier of G
(a ") * c4 is Element of the carrier of G
the multF of G . ((a "),c4) is Element of the carrier of G
[(a "),c4] is set
{(a "),c4} is non empty finite set
{{(a "),c4},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),c4] is set
((a ") * c4) * a is Element of the carrier of G
the multF of G . (((a ") * c4),a) is Element of the carrier of G
[((a ") * c4),a] is set
{((a ") * c4),a} is non empty finite set
{((a ") * c4)} is non empty finite set
{{((a ") * c4),a},{((a ") * c4)}} is non empty finite V45() set
the multF of G . [((a ") * c4),a] is set

the carrier of G is non empty set
1_ G is non being_of_order_0 Element of the carrier of G
H is Element of the carrier of G
(G,(1_ G),H) is Element of the carrier of G
H " is Element of the carrier of G
(H ") * (1_ G) is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((H "),(1_ G)) is Element of the carrier of G
[(H "),(1_ G)] is set
{(H "),(1_ G)} is non empty finite set
{(H ")} is non empty finite set
{{(H "),(1_ G)},{(H ")}} is non empty finite V45() set
the multF of G . [(H "),(1_ G)] is set
((H ") * (1_ G)) * H is Element of the carrier of G
the multF of G . (((H ") * (1_ G)),H) is Element of the carrier of G
[((H ") * (1_ G)),H] is set
{((H ") * (1_ G)),H} is non empty finite set
{((H ") * (1_ G))} is non empty finite set
{{((H ") * (1_ G)),H},{((H ") * (1_ G))}} is non empty finite V45() set
the multF of G . [((H ") * (1_ G)),H] is set
(H ") * H is Element of the carrier of G
the multF of G . ((H "),H) is Element of the carrier of G
[(H "),H] is set
{(H "),H} is non empty finite set
{{(H "),H},{(H ")}} is non empty finite V45() set
the multF of G . [(H "),H] is set

the carrier of G is non empty set
1_ G is non being_of_order_0 Element of the carrier of G
H is Element of the carrier of G
a is Element of the carrier of G
(G,H,a) is Element of the carrier of G
a " is Element of the carrier of G
(a ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((a "),H) is Element of the carrier of G
[(a "),H] is set
{(a "),H} is non empty finite set
{(a ")} is non empty finite set
{{(a "),H},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),H] is set
((a ") * H) * a is Element of the carrier of G
the multF of G . (((a ") * H),a) is Element of the carrier of G
[((a ") * H),a] is set
{((a ") * H),a} is non empty finite set
{((a ") * H)} is non empty finite set
{{((a ") * H),a},{((a ") * H)}} is non empty finite V45() set
the multF of G . [((a ") * H),a] is set

the carrier of G is non empty set
1_ G is non being_of_order_0 Element of the carrier of G
H is Element of the carrier of G
(G,H,(1_ G)) is Element of the carrier of G
(1_ G) " is Element of the carrier of G
((1_ G) ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (((1_ G) "),H) is Element of the carrier of G
[((1_ G) "),H] is set
{((1_ G) "),H} is non empty finite set
{((1_ G) ")} is non empty finite set
{{((1_ G) "),H},{((1_ G) ")}} is non empty finite V45() set
the multF of G . [((1_ G) "),H] is set
(((1_ G) ") * H) * (1_ G) is Element of the carrier of G
the multF of G . ((((1_ G) ") * H),(1_ G)) is Element of the carrier of G
[(((1_ G) ") * H),(1_ G)] is set
{(((1_ G) ") * H),(1_ G)} is non empty finite set
{(((1_ G) ") * H)} is non empty finite set
{{(((1_ G) ") * H),(1_ G)},{(((1_ G) ") * H)}} is non empty finite V45() set
the multF of G . [(((1_ G) ") * H),(1_ G)] is set
(1_ G) * H is Element of the carrier of G
the multF of G . ((1_ G),H) is Element of the carrier of G
[(1_ G),H] is set
{(1_ G),H} is non empty finite set
{(1_ G)} is non empty finite set
{{(1_ G),H},{(1_ G)}} is non empty finite V45() set
the multF of G . [(1_ G),H] is set

the carrier of G is non empty set
H is Element of the carrier of G
(G,H,H) is Element of the carrier of G
H " is Element of the carrier of G
(H ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((H "),H) is Element of the carrier of G
[(H "),H] is set
{(H "),H} is non empty finite set
{(H ")} is non empty finite set
{{(H "),H},{(H ")}} is non empty finite V45() set
the multF of G . [(H "),H] is set
((H ") * H) * H is Element of the carrier of G
the multF of G . (((H ") * H),H) is Element of the carrier of G
[((H ") * H),H] is set
{((H ") * H),H} is non empty finite set
{((H ") * H)} is non empty finite set
{{((H ") * H),H},{((H ") * H)}} is non empty finite V45() set
the multF of G . [((H ") * H),H] is set
1_ G is non being_of_order_0 Element of the carrier of G
(1_ G) * H is Element of the carrier of G
the multF of G . ((1_ G),H) is Element of the carrier of G
[(1_ G),H] is set
{(1_ G),H} is non empty finite set
{(1_ G)} is non empty finite set
{{(1_ G),H},{(1_ G)}} is non empty finite V45() set
the multF of G . [(1_ G),H] is set

the carrier of G is non empty set

the carrier of a is non empty set
H is Element of the carrier of G
H " is Element of the carrier of G
(G,H,(H ")) is Element of the carrier of G
(H ") " is Element of the carrier of G
((H ") ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (((H ") "),H) is Element of the carrier of G
[((H ") "),H] is set
{((H ") "),H} is non empty finite set
{((H ") ")} is non empty finite set
{{((H ") "),H},{((H ") ")}} is non empty finite V45() set
the multF of G . [((H ") "),H] is set
(((H ") ") * H) * (H ") is Element of the carrier of G
the multF of G . ((((H ") ") * H),(H ")) is Element of the carrier of G
[(((H ") ") * H),(H ")] is set
{(((H ") ") * H),(H ")} is non empty finite set
{(((H ") ") * H)} is non empty finite set
{{(((H ") ") * H),(H ")},{(((H ") ") * H)}} is non empty finite V45() set
the multF of G . [(((H ") ") * H),(H ")] is set
c4 is Element of the carrier of a
c4 " is Element of the carrier of a
(a,(c4 "),c4) is Element of the carrier of a
(c4 ") * (c4 ") is Element of the carrier of a
the multF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like V28([: the carrier of a, the carrier of a:], the carrier of a) associative Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the multF of a . ((c4 "),(c4 ")) is Element of the carrier of a
[(c4 "),(c4 ")] is set
{(c4 "),(c4 ")} is non empty finite set
{(c4 ")} is non empty finite set
{{(c4 "),(c4 ")},{(c4 ")}} is non empty finite V45() set
the multF of a . [(c4 "),(c4 ")] is set
((c4 ") * (c4 ")) * c4 is Element of the carrier of a
the multF of a . (((c4 ") * (c4 ")),c4) is Element of the carrier of a
[((c4 ") * (c4 ")),c4] is set
{((c4 ") * (c4 ")),c4} is non empty finite set
{((c4 ") * (c4 "))} is non empty finite set
{{((c4 ") * (c4 ")),c4},{((c4 ") * (c4 "))}} is non empty finite V45() set
the multF of a . [((c4 ") * (c4 ")),c4] is set

the carrier of G is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
(G,H,a) is Element of the carrier of G
a " is Element of the carrier of G
(a ") * H is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . ((a "),H) is Element of the carrier of G
[(a "),H] is set
{(a "),H} is non empty finite set
{(a ")} is non empty finite set
{{(a "),H},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),H] is set
((a ") * H) * a is Element of the carrier of G
the multF of G . (((a ") * H),a) is Element of the carrier of G
[((a ") * H),a] is set
{((a ") * H),a} is non empty finite set
{((a ") * H)} is non empty finite set
{{((a ") * H),a},{((a ") * H)}} is non empty finite V45() set
the multF of G . [((a ") * H),a] is set
H * a is Element of the carrier of G
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
a * H is Element of the carrier of G
the multF of G . (a,H) is Element of the carrier of G
[a,H] is set
{a,H} is non empty finite set
{a} is non empty finite set
{{a,H},{a}} is non empty finite V45() set
the multF of G . [a,H] is set
(a ") * (H * a) is Element of the carrier of G
the multF of G . ((a "),(H * a)) is Element of the carrier of G
[(a "),(H * a)] is set
{(a "),(H * a)} is non empty finite set
{{(a "),(H * a)},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),(H * a)] is set
(a ") * (H * a) is Element of the carrier of G
the multF of G . ((a "),(H * a)) is Element of the carrier of G
[(a "),(H * a)] is set
{(a "),(H * a)} is non empty finite set
{{(a "),(H * a)},{(a ")}} is non empty finite V45() set
the multF of G . [(a "),(H * a)] is set

the carrier of G is non empty set
H is Element of the carrier of G
a is Element of the carrier of G
H * a is Element of the carrier of G
the multF of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V28([: the carrier of G, the carrier of G:], the carrier of G) associative Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is non empty set
the multF of G . (H,a) is Element of the carrier of G
[H,a] is set
{H,a} is non empty finite set
{H} is non empty finite set
{{H,a},{H}} is non empty finite V45() set
the multF of G . [H,a] is set
c4 is Element of the carrier of G
(G,(H * a),c4) is Element of the carrier of G
c4 " is Element of the carrier of G
(c4 ") * (H * a) is Element of the carrier of G
the multF of G . ((c4 "),(H * a)) is Element of the carrier of G
[(c4 "),(H * a)] is set
{(c4 "),(H * a)} is non empty finite set
{(c4 ")} is non empty finite set
{{(c4 "),(H * a)},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),(H * a)] is set
((c4 ") * (H * a)) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * (H * a)),c4) is Element of the carrier of G
[((c4 ") * (H * a)),c4] is set
{((c4 ") * (H * a)),c4} is non empty finite set
{((c4 ") * (H * a))} is non empty finite set
{{((c4 ") * (H * a)),c4},{((c4 ") * (H * a))}} is non empty finite V45() set
the multF of G . [((c4 ") * (H * a)),c4] is set
(G,H,c4) is Element of the carrier of G
(c4 ") * H is Element of the carrier of G
the multF of G . ((c4 "),H) is Element of the carrier of G
[(c4 "),H] is set
{(c4 "),H} is non empty finite set
{{(c4 "),H},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),H] is set
((c4 ") * H) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * H),c4) is Element of the carrier of G
[((c4 ") * H),c4] is set
{((c4 ") * H),c4} is non empty finite set
{((c4 ") * H)} is non empty finite set
{{((c4 ") * H),c4},{((c4 ") * H)}} is non empty finite V45() set
the multF of G . [((c4 ") * H),c4] is set
(G,a,c4) is Element of the carrier of G
(c4 ") * a is Element of the carrier of G
the multF of G . ((c4 "),a) is Element of the carrier of G
[(c4 "),a] is set
{(c4 "),a} is non empty finite set
{{(c4 "),a},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),a] is set
((c4 ") * a) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * a),c4) is Element of the carrier of G
[((c4 ") * a),c4] is set
{((c4 ") * a),c4} is non empty finite set
{((c4 ") * a)} is non empty finite set
{{((c4 ") * a),c4},{((c4 ") * a)}} is non empty finite V45() set
the multF of G . [((c4 ") * a),c4] is set
(G,H,c4) * (G,a,c4) is Element of the carrier of G
the multF of G . ((G,H,c4),(G,a,c4)) is Element of the carrier of G
[(G,H,c4),(G,a,c4)] is set
{(G,H,c4),(G,a,c4)} is non empty finite set
{(G,H,c4)} is non empty finite set
{{(G,H,c4),(G,a,c4)},{(G,H,c4)}} is non empty finite V45() set
the multF of G . [(G,H,c4),(G,a,c4)] is set
1_ G is non being_of_order_0 Element of the carrier of G
H * (1_ G) is Element of the carrier of G
the multF of G . (H,(1_ G)) is Element of the carrier of G
[H,(1_ G)] is set
{H,(1_ G)} is non empty finite set
{{H,(1_ G)},{H}} is non empty finite V45() set
the multF of G . [H,(1_ G)] is set
(H * (1_ G)) * a is Element of the carrier of G
the multF of G . ((H * (1_ G)),a) is Element of the carrier of G
[(H * (1_ G)),a] is set
{(H * (1_ G)),a} is non empty finite set
{(H * (1_ G))} is non empty finite set
{{(H * (1_ G)),a},{(H * (1_ G))}} is non empty finite V45() set
the multF of G . [(H * (1_ G)),a] is set
(c4 ") * ((H * (1_ G)) * a) is Element of the carrier of G
the multF of G . ((c4 "),((H * (1_ G)) * a)) is Element of the carrier of G
[(c4 "),((H * (1_ G)) * a)] is set
{(c4 "),((H * (1_ G)) * a)} is non empty finite set
{{(c4 "),((H * (1_ G)) * a)},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),((H * (1_ G)) * a)] is set
((c4 ") * ((H * (1_ G)) * a)) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * ((H * (1_ G)) * a)),c4) is Element of the carrier of G
[((c4 ") * ((H * (1_ G)) * a)),c4] is set
{((c4 ") * ((H * (1_ G)) * a)),c4} is non empty finite set
{((c4 ") * ((H * (1_ G)) * a))} is non empty finite set
{{((c4 ") * ((H * (1_ G)) * a)),c4},{((c4 ") * ((H * (1_ G)) * a))}} is non empty finite V45() set
the multF of G . [((c4 ") * ((H * (1_ G)) * a)),c4] is set
c4 * (c4 ") is Element of the carrier of G
the multF of G . (c4,(c4 ")) is Element of the carrier of G
[c4,(c4 ")] is set
{c4,(c4 ")} is non empty finite set
{c4} is non empty finite set
{{c4,(c4 ")},{c4}} is non empty finite V45() set
the multF of G . [c4,(c4 ")] is set
H * (c4 * (c4 ")) is Element of the carrier of G
the multF of G . (H,(c4 * (c4 "))) is Element of the carrier of G
[H,(c4 * (c4 "))] is set
{H,(c4 * (c4 "))} is non empty finite set
{{H,(c4 * (c4 "))},{H}} is non empty finite V45() set
the multF of G . [H,(c4 * (c4 "))] is set
(H * (c4 * (c4 "))) * a is Element of the carrier of G
the multF of G . ((H * (c4 * (c4 "))),a) is Element of the carrier of G
[(H * (c4 * (c4 "))),a] is set
{(H * (c4 * (c4 "))),a} is non empty finite set
{(H * (c4 * (c4 ")))} is non empty finite set
{{(H * (c4 * (c4 "))),a},{(H * (c4 * (c4 ")))}} is non empty finite V45() set
the multF of G . [(H * (c4 * (c4 "))),a] is set
(c4 ") * ((H * (c4 * (c4 "))) * a) is Element of the carrier of G
the multF of G . ((c4 "),((H * (c4 * (c4 "))) * a)) is Element of the carrier of G
[(c4 "),((H * (c4 * (c4 "))) * a)] is set
{(c4 "),((H * (c4 * (c4 "))) * a)} is non empty finite set
{{(c4 "),((H * (c4 * (c4 "))) * a)},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),((H * (c4 * (c4 "))) * a)] is set
((c4 ") * ((H * (c4 * (c4 "))) * a)) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * ((H * (c4 * (c4 "))) * a)),c4) is Element of the carrier of G
[((c4 ") * ((H * (c4 * (c4 "))) * a)),c4] is set
{((c4 ") * ((H * (c4 * (c4 "))) * a)),c4} is non empty finite set
{((c4 ") * ((H * (c4 * (c4 "))) * a))} is non empty finite set
{{((c4 ") * ((H * (c4 * (c4 "))) * a)),c4},{((c4 ") * ((H * (c4 * (c4 "))) * a))}} is non empty finite V45() set
the multF of G . [((c4 ") * ((H * (c4 * (c4 "))) * a)),c4] is set
H * c4 is Element of the carrier of G
the multF of G . (H,c4) is Element of the carrier of G
[H,c4] is set
{H,c4} is non empty finite set
{{H,c4},{H}} is non empty finite V45() set
the multF of G . [H,c4] is set
(H * c4) * (c4 ") is Element of the carrier of G
the multF of G . ((H * c4),(c4 ")) is Element of the carrier of G
[(H * c4),(c4 ")] is set
{(H * c4),(c4 ")} is non empty finite set
{(H * c4)} is non empty finite set
{{(H * c4),(c4 ")},{(H * c4)}} is non empty finite V45() set
the multF of G . [(H * c4),(c4 ")] is set
((H * c4) * (c4 ")) * a is Element of the carrier of G
the multF of G . (((H * c4) * (c4 ")),a) is Element of the carrier of G
[((H * c4) * (c4 ")),a] is set
{((H * c4) * (c4 ")),a} is non empty finite set
{((H * c4) * (c4 "))} is non empty finite set
{{((H * c4) * (c4 ")),a},{((H * c4) * (c4 "))}} is non empty finite V45() set
the multF of G . [((H * c4) * (c4 ")),a] is set
(c4 ") * (((H * c4) * (c4 ")) * a) is Element of the carrier of G
the multF of G . ((c4 "),(((H * c4) * (c4 ")) * a)) is Element of the carrier of G
[(c4 "),(((H * c4) * (c4 ")) * a)] is set
{(c4 "),(((H * c4) * (c4 ")) * a)} is non empty finite set
{{(c4 "),(((H * c4) * (c4 ")) * a)},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),(((H * c4) * (c4 ")) * a)] is set
((c4 ") * (((H * c4) * (c4 ")) * a)) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * (((H * c4) * (c4 ")) * a)),c4) is Element of the carrier of G
[((c4 ") * (((H * c4) * (c4 ")) * a)),c4] is set
{((c4 ") * (((H * c4) * (c4 ")) * a)),c4} is non empty finite set
{((c4 ") * (((H * c4) * (c4 ")) * a))} is non empty finite set
{{((c4 ") * (((H * c4) * (c4 ")) * a)),c4},{((c4 ") * (((H * c4) * (c4 ")) * a))}} is non empty finite V45() set
the multF of G . [((c4 ") * (((H * c4) * (c4 ")) * a)),c4] is set
(H * c4) * ((c4 ") * a) is Element of the carrier of G
the multF of G . ((H * c4),((c4 ") * a)) is Element of the carrier of G
[(H * c4),((c4 ") * a)] is set
{(H * c4),((c4 ") * a)} is non empty finite set
{{(H * c4),((c4 ") * a)},{(H * c4)}} is non empty finite V45() set
the multF of G . [(H * c4),((c4 ") * a)] is set
(c4 ") * ((H * c4) * ((c4 ") * a)) is Element of the carrier of G
the multF of G . ((c4 "),((H * c4) * ((c4 ") * a))) is Element of the carrier of G
[(c4 "),((H * c4) * ((c4 ") * a))] is set
{(c4 "),((H * c4) * ((c4 ") * a))} is non empty finite set
{{(c4 "),((H * c4) * ((c4 ") * a))},{(c4 ")}} is non empty finite V45() set
the multF of G . [(c4 "),((H * c4) * ((c4 ") * a))] is set
((c4 ") * ((H * c4) * ((c4 ") * a))) * c4 is Element of the carrier of G
the multF of G . (((c4 ") * ((H * c4) * ((c4 ") * a))),c4) is Element of the carrier of G
[((c4 ") * ((H * c4) * ((c4 ") * a))),c4] is set
{((c4 ") * ((H * c4) * ((c4 ") * a))),c4} is non empty finite set
{((c4 ") * ((H * c4) * ((c4 ") * a)))} is non empty finite set
{{((c4 ") * ((H * c4) * ((c4 ") * a))),c4},{((c4 ") * ((H * c4) * ((c4 ") * a)))}} is non empty finite V45() set
the multF of G . [((c4 ") * ((H * c4) * ((c4 ") * a))),c4] is set
(c4 ") * (H * c4) is Element of the carrier of G
the multF of G . ((c4 "),(H * c4)) is Element of the carrier of G
[(c4 "),(H * c4)] is set
{(c4 "),(H * c4)} is non empty finite set
{{(c4 "),(H * c4)},{(c4 ")}} is non empty finite V45() set
the multF of G .