:: BCIALG_6 semantic presentation

REAL is set
NAT is non empty V24() V25() V26() Element of bool REAL
bool REAL is set
NAT is non empty V24() V25() V26() set
bool NAT is set
COMPLEX is set
RAT is set
INT is set
[:COMPLEX,COMPLEX:] is set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is set
[:[:NAT,NAT:],NAT:] is set
bool [:[:NAT,NAT:],NAT:] is set
bool NAT is set
{} is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative set
the empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative set is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative set
1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
0 is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative Element of NAT
K186(1) is V92() V93() integer ext-real non positive set
X is set
[:NAT,X:] is set
bool [:NAT,X:] is set
G is Relation-like NAT -defined X -valued Function-like quasi_total Element of bool [:NAT,X:]
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
G . K is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
G . RK is Element of X
X is non empty BCIStr_0
the carrier of X is non empty set
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
0. X is V47(X) Element of the carrier of X
the ZeroF of X is Element of the carrier of X
[:NAT, the carrier of X:] is set
bool [:NAT, the carrier of X:] is set
G is set
K is Element of the carrier of X
RK is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,RK,0) is Element of the carrier of X
K1 is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
( the carrier of X,RK,(RK1 + 1)) is Element of the carrier of X
( the carrier of X,RK,RK1) is Element of the carrier of X
( the carrier of X,RK,RK1) ` is Element of the carrier of X
(0. X) \ ( the carrier of X,RK,RK1) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),( the carrier of X,RK,RK1)) is Element of the carrier of X
[(0. X),( the carrier of X,RK,RK1)] is set
{(0. X),( the carrier of X,RK,RK1)} is non empty set
{(0. X)} is non empty set
{{(0. X),( the carrier of X,RK,RK1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),( the carrier of X,RK,RK1)] is set
K \ (( the carrier of X,RK,RK1) `) is Element of the carrier of X
the InternalDiff of X . (K,(( the carrier of X,RK,RK1) `)) is Element of the carrier of X
[K,(( the carrier of X,RK,RK1) `)] is set
{K,(( the carrier of X,RK,RK1) `)} is non empty set
{K} is non empty set
{{K,(( the carrier of X,RK,RK1) `)},{K}} is non empty set
the InternalDiff of X . [K,(( the carrier of X,RK,RK1) `)] is set
G is Relation-like Function-like set
dom G is set
K is Element of the carrier of X
G . K is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 is Element of the carrier of X
K1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,K1,0) is Element of the carrier of X
( the carrier of X,K1,RK) is Element of the carrier of X
K is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
RK is Element of the carrier of X
K . (RK,0) is Element of the carrier of X
[RK,0] is set
{RK,0} is non empty set
{RK} is non empty set
{{RK,0},{RK}} is non empty set
K . [RK,0] is set
G . RK is set
K1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,K1,0) is Element of the carrier of X
I is Element of the carrier of X
RK1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,RK1,0) is Element of the carrier of X
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
K . (RK,(K1 + 1)) is Element of the carrier of X
[RK,(K1 + 1)] is set
{RK,(K1 + 1)} is non empty set
{{RK,(K1 + 1)},{RK}} is non empty set
K . [RK,(K1 + 1)] is set
K . (RK,K1) is Element of the carrier of X
[RK,K1] is set
{RK,K1} is non empty set
{{RK,K1},{RK}} is non empty set
K . [RK,K1] is set
(K . (RK,K1)) ` is Element of the carrier of X
(0. X) \ (K . (RK,K1)) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(K . (RK,K1))) is Element of the carrier of X
[(0. X),(K . (RK,K1))] is set
{(0. X),(K . (RK,K1))} is non empty set
{(0. X)} is non empty set
{{(0. X),(K . (RK,K1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(K . (RK,K1))] is set
RK \ ((K . (RK,K1)) `) is Element of the carrier of X
the InternalDiff of X . (RK,((K . (RK,K1)) `)) is Element of the carrier of X
[RK,((K . (RK,K1)) `)] is set
{RK,((K . (RK,K1)) `)} is non empty set
{{RK,((K . (RK,K1)) `)},{RK}} is non empty set
the InternalDiff of X . [RK,((K . (RK,K1)) `)] is set
RK1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,RK1,K1) is Element of the carrier of X
I is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,I,(K1 + 1)) is Element of the carrier of X
f is Element of the carrier of X
RI is Relation-like NAT -defined the carrier of X -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of X:]
( the carrier of X,RI,0) is Element of the carrier of X
G is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
K is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
RK is Element of the carrier of X
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
[RK,RK1] is set
{RK,RK1} is non empty set
{RK} is non empty set
{{RK,RK1},{RK}} is non empty set
G . [RK,RK1] is set
K . [RK,RK1] is set
K . (RK,RK1) is Element of the carrier of X
RK1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
[RK,(RK1 + 1)] is set
{RK,(RK1 + 1)} is non empty set
{{RK,(RK1 + 1)},{RK}} is non empty set
G . [RK,(RK1 + 1)] is set
G . (RK,(RK1 + 1)) is Element of the carrier of X
G . (RK,RK1) is Element of the carrier of X
(G . (RK,RK1)) ` is Element of the carrier of X
(0. X) \ (G . (RK,RK1)) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(G . (RK,RK1))) is Element of the carrier of X
[(0. X),(G . (RK,RK1))] is set
{(0. X),(G . (RK,RK1))} is non empty set
{(0. X)} is non empty set
{{(0. X),(G . (RK,RK1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G . (RK,RK1))] is set
RK \ ((G . (RK,RK1)) `) is Element of the carrier of X
the InternalDiff of X . (RK,((G . (RK,RK1)) `)) is Element of the carrier of X
[RK,((G . (RK,RK1)) `)] is set
{RK,((G . (RK,RK1)) `)} is non empty set
{{RK,((G . (RK,RK1)) `)},{RK}} is non empty set
the InternalDiff of X . [RK,((G . (RK,RK1)) `)] is set
K . (RK,(RK1 + 1)) is Element of the carrier of X
K . [RK,(RK1 + 1)] is set
[RK,0] is set
{RK,0} is non empty set
{{RK,0},{RK}} is non empty set
G . [RK,0] is set
G . (RK,0) is Element of the carrier of X
K . (RK,0) is Element of the carrier of X
K . [RK,0] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
G . (RK,K1) is Element of the carrier of X
[RK,K1] is set
{RK,K1} is non empty set
{{RK,K1},{RK}} is non empty set
G . [RK,K1] is set
K . (RK,K1) is Element of the carrier of X
K . [RK,K1] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is V92() V93() integer ext-real set
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
K is Element of the carrier of X
abs G is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . (K,(abs G)) is Element of the carrier of X
[K,(abs G)] is set
{K,(abs G)} is non empty set
{K} is non empty set
{{K,(abs G)},{K}} is non empty set
(X) . [K,(abs G)] is set
K ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ K is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),K) is Element of the carrier of X
[(0. X),K] is set
{(0. X),K} is non empty set
{(0. X)} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K] is set
(X) . ((K `),(abs G)) is Element of the carrier of X
[(K `),(abs G)] is set
{(K `),(abs G)} is non empty set
{(K `)} is non empty set
{{(K `),(abs G)},{(K `)}} is non empty set
(X) . [(K `),(abs G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K is Element of the carrier of X
(X,G,K) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (K,G) is set
[K,G] is set
{K,G} is non empty set
{K} is non empty set
{{K,G},{K}} is non empty set
(X) . [K,G] is set
RK is Element of the carrier of X
abs G is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of the carrier of X
K is Element of AtomSet X
G \ K is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (G,K) is Element of the carrier of X
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
the InternalDiff of X . [G,K] is set
RK is Element of AtomSet X
G \ RK is Element of the carrier of X
the InternalDiff of X . (G,RK) is Element of the carrier of X
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
the InternalDiff of X . [G,RK] is set
K \ (G \ RK) is Element of the carrier of X
the InternalDiff of X . (K,(G \ RK)) is Element of the carrier of X
[K,(G \ RK)] is set
{K,(G \ RK)} is non empty set
{K} is non empty set
{{K,(G \ RK)},{K}} is non empty set
the InternalDiff of X . [K,(G \ RK)] is set
RK \ (G \ K) is Element of the carrier of X
the InternalDiff of X . (RK,(G \ K)) is Element of the carrier of X
[RK,(G \ K)] is set
{RK,(G \ K)} is non empty set
{RK} is non empty set
{{RK,(G \ K)},{RK}} is non empty set
the InternalDiff of X . [RK,(G \ K)] is set
G \ (G \ RK) is Element of the carrier of X
the InternalDiff of X . (G,(G \ RK)) is Element of the carrier of X
[G,(G \ RK)] is set
{G,(G \ RK)} is non empty set
{{G,(G \ RK)},{G}} is non empty set
the InternalDiff of X . [G,(G \ RK)] is set
(G \ (G \ RK)) \ RK is Element of the carrier of X
the InternalDiff of X . ((G \ (G \ RK)),RK) is Element of the carrier of X
[(G \ (G \ RK)),RK] is set
{(G \ (G \ RK)),RK} is non empty set
{(G \ (G \ RK))} is non empty set
{{(G \ (G \ RK)),RK},{(G \ (G \ RK))}} is non empty set
the InternalDiff of X . [(G \ (G \ RK)),RK] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(RK \ (G \ K)) \ (K \ (G \ RK)) is Element of the carrier of X
the InternalDiff of X . ((RK \ (G \ K)),(K \ (G \ RK))) is Element of the carrier of X
[(RK \ (G \ K)),(K \ (G \ RK))] is set
{(RK \ (G \ K)),(K \ (G \ RK))} is non empty set
{(RK \ (G \ K))} is non empty set
{{(RK \ (G \ K)),(K \ (G \ RK))},{(RK \ (G \ K))}} is non empty set
the InternalDiff of X . [(RK \ (G \ K)),(K \ (G \ RK))] is set
(G \ (G \ RK)) \ (G \ K) is Element of the carrier of X
the InternalDiff of X . ((G \ (G \ RK)),(G \ K)) is Element of the carrier of X
[(G \ (G \ RK)),(G \ K)] is set
{(G \ (G \ RK)),(G \ K)} is non empty set
{{(G \ (G \ RK)),(G \ K)},{(G \ (G \ RK))}} is non empty set
the InternalDiff of X . [(G \ (G \ RK)),(G \ K)] is set
((G \ (G \ RK)) \ (G \ K)) \ (K \ (G \ RK)) is Element of the carrier of X
the InternalDiff of X . (((G \ (G \ RK)) \ (G \ K)),(K \ (G \ RK))) is Element of the carrier of X
[((G \ (G \ RK)) \ (G \ K)),(K \ (G \ RK))] is set
{((G \ (G \ RK)) \ (G \ K)),(K \ (G \ RK))} is non empty set
{((G \ (G \ RK)) \ (G \ K))} is non empty set
{{((G \ (G \ RK)) \ (G \ K)),(K \ (G \ RK))},{((G \ (G \ RK)) \ (G \ K))}} is non empty set
the InternalDiff of X . [((G \ (G \ RK)) \ (G \ K)),(K \ (G \ RK))] is set
K1 is Element of the carrier of X
G \ (G \ K) is Element of the carrier of X
the InternalDiff of X . (G,(G \ K)) is Element of the carrier of X
[G,(G \ K)] is set
{G,(G \ K)} is non empty set
{{G,(G \ K)},{G}} is non empty set
the InternalDiff of X . [G,(G \ K)] is set
(G \ (G \ K)) \ (G \ RK) is Element of the carrier of X
the InternalDiff of X . ((G \ (G \ K)),(G \ RK)) is Element of the carrier of X
[(G \ (G \ K)),(G \ RK)] is set
{(G \ (G \ K)),(G \ RK)} is non empty set
{(G \ (G \ K))} is non empty set
{{(G \ (G \ K)),(G \ RK)},{(G \ (G \ K))}} is non empty set
the InternalDiff of X . [(G \ (G \ K)),(G \ RK)] is set
((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK)) is Element of the carrier of X
the InternalDiff of X . (((G \ (G \ K)) \ (G \ RK)),(K \ (G \ RK))) is Element of the carrier of X
[((G \ (G \ K)) \ (G \ RK)),(K \ (G \ RK))] is set
{((G \ (G \ K)) \ (G \ RK)),(K \ (G \ RK))} is non empty set
{((G \ (G \ K)) \ (G \ RK))} is non empty set
{{((G \ (G \ K)) \ (G \ RK)),(K \ (G \ RK))},{((G \ (G \ K)) \ (G \ RK))}} is non empty set
the InternalDiff of X . [((G \ (G \ K)) \ (G \ RK)),(K \ (G \ RK))] is set
(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),(0. X)) is Element of the carrier of X
[(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),(0. X)] is set
{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),(0. X)} is non empty set
{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK)))} is non empty set
{{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),(0. X)},{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK)))}} is non empty set
the InternalDiff of X . [(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),(0. X)] is set
(G \ (G \ K)) \ K is Element of the carrier of X
the InternalDiff of X . ((G \ (G \ K)),K) is Element of the carrier of X
[(G \ (G \ K)),K] is set
{(G \ (G \ K)),K} is non empty set
{{(G \ (G \ K)),K},{(G \ (G \ K))}} is non empty set
the InternalDiff of X . [(G \ (G \ K)),K] is set
(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))) \ ((G \ (G \ K)) \ K) is Element of the carrier of X
the InternalDiff of X . ((((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),((G \ (G \ K)) \ K)) is Element of the carrier of X
[(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),((G \ (G \ K)) \ K)] is set
{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),((G \ (G \ K)) \ K)} is non empty set
{{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),((G \ (G \ K)) \ K)},{(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK)))}} is non empty set
the InternalDiff of X . [(((G \ (G \ K)) \ (G \ RK)) \ (K \ (G \ RK))),((G \ (G \ K)) \ K)] is set
(K \ (G \ RK)) \ (RK \ (G \ K)) is Element of the carrier of X
the InternalDiff of X . ((K \ (G \ RK)),(RK \ (G \ K))) is Element of the carrier of X
[(K \ (G \ RK)),(RK \ (G \ K))] is set
{(K \ (G \ RK)),(RK \ (G \ K))} is non empty set
{(K \ (G \ RK))} is non empty set
{{(K \ (G \ RK)),(RK \ (G \ K))},{(K \ (G \ RK))}} is non empty set
the InternalDiff of X . [(K \ (G \ RK)),(RK \ (G \ K))] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K + 1),G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,(K + 1)) is set
[G,(K + 1)] is set
{G,(K + 1)} is non empty set
{G} is non empty set
{{G,(K + 1)},{G}} is non empty set
(X) . [G,(K + 1)] is set
(X,K,G) is Element of the carrier of X
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
G \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,K,G) `)) is Element of the carrier of X
[G,((X,K,G) `)] is set
{G,((X,K,G) `)} is non empty set
{{G,((X,K,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,K,G) `)] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK + 1),G) is Element of the carrier of X
(X) . (G,(RK + 1)) is set
[G,(RK + 1)] is set
{G,(RK + 1)} is non empty set
{{G,(RK + 1)},{G}} is non empty set
(X) . [G,(RK + 1)] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
G \ ((X,RK,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,RK,G) `)) is Element of the carrier of X
[G,((X,RK,G) `)] is set
{G,((X,RK,G) `)} is non empty set
{{G,((X,RK,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,RK,G) `)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,1) is set
[G,1] is set
{G,1} is non empty set
{G} is non empty set
{{G,1},{G}} is non empty set
(X) . [G,1] is set
0 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(0 + 1),G) is Element of the carrier of X
(X) . (G,(0 + 1)) is set
[G,(0 + 1)] is set
{G,(0 + 1)} is non empty set
{{G,(0 + 1)},{G}} is non empty set
(X) . [G,(0 + 1)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,0,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,0,G)) is Element of the carrier of X
[(0. X),(X,0,G)] is set
{(0. X),(X,0,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,0,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,0,G)] is set
G \ ((X,0,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,0,G) `)) is Element of the carrier of X
[G,((X,0,G) `)] is set
{G,((X,0,G) `)} is non empty set
{{G,((X,0,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,0,G) `)] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
G \ ((0. X) `) is Element of the carrier of X
the InternalDiff of X . (G,((0. X) `)) is Element of the carrier of X
[G,((0. X) `)] is set
{G,((0. X) `)} is non empty set
{{G,((0. X) `)},{G}} is non empty set
the InternalDiff of X . [G,((0. X) `)] is set
G \ (0. X) is Element of the carrier of X
the InternalDiff of X . (G,(0. X)) is Element of the carrier of X
[G,(0. X)] is set
{G,(0. X)} is non empty set
{{G,(0. X)},{G}} is non empty set
the InternalDiff of X . [G,(0. X)] is set
- 1 is V92() V93() integer ext-real non positive Element of INT
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,(- 1),G) is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
abs (- 1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (- 1))) is Element of the carrier of X
[(G `),(abs (- 1))] is set
{(G `),(abs (- 1))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (- 1))},{(G `)}} is non empty set
(X) . [(G `),(abs (- 1))] is set
- (- 1) is V92() V93() integer ext-real non negative Element of INT
(X) . ((G `),(- (- 1))) is set
[(G `),(- (- 1))] is set
{(G `),(- (- 1))} is non empty set
{{(G `),(- (- 1))},{(G `)}} is non empty set
(X) . [(G `),(- (- 1))] is set
(X,1,(G `)) is Element of the carrier of X
(X) . ((G `),1) is set
[(G `),1] is set
{(G `),1} is non empty set
{{(G `),1},{(G `)}} is non empty set
(X) . [(G `),1] is set
2 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,2,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,2) is set
[G,2] is set
{G,2} is non empty set
{G} is non empty set
{{G,2},{G}} is non empty set
(X) . [G,2] is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
G \ (G `) is Element of the carrier of X
the InternalDiff of X . (G,(G `)) is Element of the carrier of X
[G,(G `)] is set
{G,(G `)} is non empty set
{{G,(G `)},{G}} is non empty set
the InternalDiff of X . [G,(G `)] is set
1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(1 + 1),G) is Element of the carrier of X
(X) . (G,(1 + 1)) is set
[G,(1 + 1)] is set
{G,(1 + 1)} is non empty set
{{G,(1 + 1)},{G}} is non empty set
(X) . [G,(1 + 1)] is set
(X,1,G) is Element of the carrier of X
(X) . (G,1) is set
[G,1] is set
{G,1} is non empty set
{{G,1},{G}} is non empty set
(X) . [G,1] is set
(X,1,G) ` is Element of the carrier of X
(0. X) \ (X,1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,1,G)) is Element of the carrier of X
[(0. X),(X,1,G)] is set
{(0. X),(X,1,G)} is non empty set
{{(0. X),(X,1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,1,G)] is set
G \ ((X,1,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,1,G) `)) is Element of the carrier of X
[G,((X,1,G) `)] is set
{G,((X,1,G) `)} is non empty set
{{G,((X,1,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,1,G) `)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the carrier of X is non empty set
the ZeroF of X is Element of the carrier of X
G is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,G,(0. X)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((0. X),G) is set
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
(X) . [(0. X),G] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,(0. X)) is Element of the carrier of X
(X) . ((0. X),K) is set
[(0. X),K] is set
{(0. X),K} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
(X) . [(0. X),K] is set
K + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K + 1),(0. X)) is Element of the carrier of X
(X) . ((0. X),(K + 1)) is set
[(0. X),(K + 1)] is set
{(0. X),(K + 1)} is non empty set
{{(0. X),(K + 1)},{(0. X)}} is non empty set
(X) . [(0. X),(K + 1)] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
((0. X) `) ` is Element of the carrier of X
(0. X) \ ((0. X) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((0. X) `)) is Element of the carrier of X
[(0. X),((0. X) `)] is set
{(0. X),((0. X) `)} is non empty set
{{(0. X),((0. X) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((0. X) `)] is set
(X,0,(0. X)) is Element of the carrier of X
(X) . ((0. X),0) is set
[(0. X),0] is set
{(0. X),0} is non empty set
{{(0. X),0},{(0. X)}} is non empty set
(X) . [(0. X),0] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G is Element of AtomSet X
(X,(- 1),G) is Element of the carrier of X
(X,(- 1),(X,(- 1),G)) is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,(- 1),(G `)) is Element of the carrier of X
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- K is V92() V93() integer ext-real non positive Element of INT
(X,(- K),G) is Element of the carrier of X
(X,(- K),((G `) `)) is Element of the carrier of X
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- RK is V92() V93() integer ext-real non positive Element of INT
(X,(- RK),G) is Element of the carrier of X
(X,(- RK),((G `) `)) is Element of the carrier of X
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
- (RK + 1) is V92() V93() integer ext-real non positive Element of INT
- (- (RK + 1)) is V92() V93() integer ext-real non negative Element of INT
(X,(- (RK + 1)),G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
abs (- (RK + 1)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (- (RK + 1)))) is Element of the carrier of X
[(G `),(abs (- (RK + 1)))] is set
{(G `),(abs (- (RK + 1)))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (- (RK + 1)))},{(G `)}} is non empty set
(X) . [(G `),(abs (- (RK + 1)))] is set
((G `) `) ` is Element of the carrier of X
(0. X) \ ((G `) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((G `) `)) is Element of the carrier of X
[(0. X),((G `) `)] is set
{(0. X),((G `) `)} is non empty set
{{(0. X),((G `) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((G `) `)] is set
(X) . ((((G `) `) `),(abs (- (RK + 1)))) is Element of the carrier of X
[(((G `) `) `),(abs (- (RK + 1)))] is set
{(((G `) `) `),(abs (- (RK + 1)))} is non empty set
{(((G `) `) `)} is non empty set
{{(((G `) `) `),(abs (- (RK + 1)))},{(((G `) `) `)}} is non empty set
(X) . [(((G `) `) `),(abs (- (RK + 1)))] is set
(X,(- (RK + 1)),((G `) `)) is Element of the carrier of X
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,((G `) `)) is Element of the carrier of X
(X) . (((G `) `),0) is set
[((G `) `),0] is set
{((G `) `),0} is non empty set
{((G `) `)} is non empty set
{{((G `) `),0},{((G `) `)}} is non empty set
(X) . [((G `) `),0] is set
- 0 is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative Element of INT
(X,(- 0),G) is Element of the carrier of X
(X) . (G,(- 0)) is set
[G,(- 0)] is set
{G,(- 0)} is non empty set
{{G,(- 0)},{G}} is non empty set
(X) . [G,(- 0)] is set
(X,(- 0),((G `) `)) is Element of the carrier of X
(X) . (((G `) `),(- 0)) is set
[((G `) `),(- 0)] is set
{((G `) `),(- 0)} is non empty set
{{((G `) `),(- 0)},{((G `) `)}} is non empty set
(X) . [((G `) `),(- 0)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),K) is set
[(G `),K] is set
{(G `),K} is non empty set
{(G `)} is non empty set
{{(G `),K},{(G `)}} is non empty set
(X) . [(G `),K] is set
- K is V92() V93() integer ext-real non positive Element of INT
(X,(- K),G) is Element of the carrier of X
- (- K) is V92() V93() integer ext-real non negative Element of INT
abs (- K) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (- K))) is Element of the carrier of X
[(G `),(abs (- K))] is set
{(G `),(abs (- K))} is non empty set
{{(G `),(abs (- K))},{(G `)}} is non empty set
(X) . [(G `),(abs (- K))] is set
(X) . ((G `),(- (- K))) is set
[(G `),(- (- K))] is set
{(G `),(- (- K))} is non empty set
{{(G `),(- (- K))},{(G `)}} is non empty set
(X) . [(G `),(- (- K))] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
G is Element of the carrier of X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK + 1),G) is Element of the carrier of X
(X) . (G,(RK + 1)) is set
[G,(RK + 1)] is set
{G,(RK + 1)} is non empty set
{{G,(RK + 1)},{G}} is non empty set
(X) . [G,(RK + 1)] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
G \ (G `) is Element of the carrier of X
the InternalDiff of X . (G,(G `)) is Element of the carrier of X
[G,(G `)] is set
{G,(G `)} is non empty set
{{G,(G `)},{G}} is non empty set
the InternalDiff of X . [G,(G `)] is set
G \ (0. X) is Element of the carrier of X
the InternalDiff of X . (G,(0. X)) is Element of the carrier of X
[G,(0. X)] is set
{G,(0. X)} is non empty set
{{G,(0. X)},{G}} is non empty set
the InternalDiff of X . [G,(0. X)] is set
K1 is Element of the carrier of X
(X,1,G) is Element of the carrier of X
(X) . (G,1) is set
[G,1] is set
{G,1} is non empty set
{{G,1},{G}} is non empty set
(X) . [G,1] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
G is Element of the carrier of X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- K is V92() V93() integer ext-real non positive Element of INT
(X,(- K),G) is Element of the carrier of X
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- RK is V92() V93() integer ext-real non positive Element of INT
(X,(- RK),G) is Element of the carrier of X
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
- (RK + 1) is V92() V93() integer ext-real non positive Element of INT
- (- (RK + 1)) is V92() V93() integer ext-real non negative Element of INT
(X,(- (RK + 1)),G) is Element of the carrier of X
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K1 is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
abs (- RK) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (- RK))) is Element of the carrier of X
[(G `),(abs (- RK))] is set
{(G `),(abs (- RK))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (- RK))},{(G `)}} is non empty set
(X) . [(G `),(abs (- RK))] is set
- (- RK) is V92() V93() integer ext-real non negative Element of INT
(X) . ((G `),(- (- RK))) is set
[(G `),(- (- RK))] is set
{(G `),(- (- RK))} is non empty set
{{(G `),(- (- RK))},{(G `)}} is non empty set
(X) . [(G `),(- (- RK))] is set
(X,RK,(G `)) is Element of the carrier of X
(X) . ((G `),RK) is set
[(G `),RK] is set
{(G `),RK} is non empty set
{{(G `),RK},{(G `)}} is non empty set
(X) . [(G `),RK] is set
(X,RK,(G `)) ` is Element of the carrier of X
(0. X) \ (X,RK,(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,(G `))) is Element of the carrier of X
[(0. X),(X,RK,(G `))] is set
{(0. X),(X,RK,(G `))} is non empty set
{{(0. X),(X,RK,(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,(G `))] is set
(G `) \ ((X,RK,(G `)) `) is Element of the carrier of X
the InternalDiff of X . ((G `),((X,RK,(G `)) `)) is Element of the carrier of X
[(G `),((X,RK,(G `)) `)] is set
{(G `),((X,RK,(G `)) `)} is non empty set
{{(G `),((X,RK,(G `)) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),((X,RK,(G `)) `)] is set
G \ (0. X) is Element of the carrier of X
the InternalDiff of X . (G,(0. X)) is Element of the carrier of X
[G,(0. X)] is set
{G,(0. X)} is non empty set
{G} is non empty set
{{G,(0. X)},{G}} is non empty set
the InternalDiff of X . [G,(0. X)] is set
(G \ (0. X)) ` is Element of the carrier of X
(0. X) \ (G \ (0. X)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ (0. X))) is Element of the carrier of X
[(0. X),(G \ (0. X))] is set
{(0. X),(G \ (0. X))} is non empty set
{{(0. X),(G \ (0. X))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ (0. X))] is set
K1 is Element of the carrier of X
(X,(RK + 1),(G `)) is Element of the carrier of X
(X) . ((G `),(RK + 1)) is set
[(G `),(RK + 1)] is set
{(G `),(RK + 1)} is non empty set
{{(G `),(RK + 1)},{(G `)}} is non empty set
(X) . [(G `),(RK + 1)] is set
(X) . ((G `),(- (- (RK + 1)))) is set
[(G `),(- (- (RK + 1)))] is set
{(G `),(- (- (RK + 1)))} is non empty set
{{(G `),(- (- (RK + 1)))},{(G `)}} is non empty set
(X) . [(G `),(- (- (RK + 1)))] is set
abs (- (RK + 1)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (- (RK + 1)))) is Element of the carrier of X
[(G `),(abs (- (RK + 1)))] is set
{(G `),(abs (- (RK + 1)))} is non empty set
{{(G `),(abs (- (RK + 1)))},{(G `)}} is non empty set
(X) . [(G `),(abs (- (RK + 1)))] is set
(X,(- (RK + 1)),G) is Element of the carrier of X
- 0 is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative Element of INT
(X,(- 0),G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,(- 0)) is set
[G,(- 0)] is set
{G,(- 0)} is non empty set
{G} is non empty set
{{G,(- 0)},{G}} is non empty set
(X) . [G,(- 0)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is V92() V93() integer ext-real set
(X,K,G) is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
RK is V92() V93() integer ext-real set
(X,RK,G) is Element of the carrier of X
RK + 1 is V92() V93() integer ext-real Element of INT
(X,(RK + 1),G) is Element of the carrier of X
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K1 + 1),G) is Element of the carrier of X
(X) . (G,(K1 + 1)) is set
[G,(K1 + 1)] is set
{G,(K1 + 1)} is non empty set
{{G,(K1 + 1)},{G}} is non empty set
(X) . [G,(K1 + 1)] is set
(X,(K1 + 1),G) ` is Element of the carrier of X
(0. X) \ (X,(K1 + 1),G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,(K1 + 1),G)) is Element of the carrier of X
[(0. X),(X,(K1 + 1),G)] is set
{(0. X),(X,(K1 + 1),G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,(K1 + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K1 + 1),G)] is set
((X,(K1 + 1),G) `) ` is Element of the carrier of X
(0. X) \ ((X,(K1 + 1),G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,(K1 + 1),G) `)) is Element of the carrier of X
[(0. X),((X,(K1 + 1),G) `)] is set
{(0. X),((X,(K1 + 1),G) `)} is non empty set
{{(0. X),((X,(K1 + 1),G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,(K1 + 1),G) `)] is set
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,K1,G) ` is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
G \ ((X,K1,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,K1,G) `)) is Element of the carrier of X
[G,((X,K1,G) `)] is set
{G,((X,K1,G) `)} is non empty set
{{G,((X,K1,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,K1,G) `)] is set
(G \ ((X,K1,G) `)) ` is Element of the carrier of X
(0. X) \ (G \ ((X,K1,G) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ ((X,K1,G) `))) is Element of the carrier of X
[(0. X),(G \ ((X,K1,G) `))] is set
{(0. X),(G \ ((X,K1,G) `))} is non empty set
{{(0. X),(G \ ((X,K1,G) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ ((X,K1,G) `))] is set
((G \ ((X,K1,G) `)) `) ` is Element of the carrier of X
(0. X) \ ((G \ ((X,K1,G) `)) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((G \ ((X,K1,G) `)) `)) is Element of the carrier of X
[(0. X),((G \ ((X,K1,G) `)) `)] is set
{(0. X),((G \ ((X,K1,G) `)) `)} is non empty set
{{(0. X),((G \ ((X,K1,G) `)) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((G \ ((X,K1,G) `)) `)] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
((X,K1,G) `) ` is Element of the carrier of X
(0. X) \ ((X,K1,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,K1,G) `)) is Element of the carrier of X
[(0. X),((X,K1,G) `)] is set
{(0. X),((X,K1,G) `)} is non empty set
{{(0. X),((X,K1,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,K1,G) `)] is set
(G `) \ (((X,K1,G) `) `) is Element of the carrier of X
the InternalDiff of X . ((G `),(((X,K1,G) `) `)) is Element of the carrier of X
[(G `),(((X,K1,G) `) `)] is set
{(G `),(((X,K1,G) `) `)} is non empty set
{(G `)} is non empty set
{{(G `),(((X,K1,G) `) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),(((X,K1,G) `) `)] is set
((G `) \ (((X,K1,G) `) `)) ` is Element of the carrier of X
(0. X) \ ((G `) \ (((X,K1,G) `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((G `) \ (((X,K1,G) `) `))) is Element of the carrier of X
[(0. X),((G `) \ (((X,K1,G) `) `))] is set
{(0. X),((G `) \ (((X,K1,G) `) `))} is non empty set
{{(0. X),((G `) \ (((X,K1,G) `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((G `) \ (((X,K1,G) `) `))] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
(((X,K1,G) `) `) ` is Element of the carrier of X
(0. X) \ (((X,K1,G) `) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(((X,K1,G) `) `)) is Element of the carrier of X
[(0. X),(((X,K1,G) `) `)] is set
{(0. X),(((X,K1,G) `) `)} is non empty set
{{(0. X),(((X,K1,G) `) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(((X,K1,G) `) `)] is set
((G `) `) \ ((((X,K1,G) `) `) `) is Element of the carrier of X
the InternalDiff of X . (((G `) `),((((X,K1,G) `) `) `)) is Element of the carrier of X
[((G `) `),((((X,K1,G) `) `) `)] is set
{((G `) `),((((X,K1,G) `) `) `)} is non empty set
{((G `) `)} is non empty set
{{((G `) `),((((X,K1,G) `) `) `)},{((G `) `)}} is non empty set
the InternalDiff of X . [((G `) `),((((X,K1,G) `) `) `)] is set
G \ ((((X,K1,G) `) `) `) is Element of the carrier of X
the InternalDiff of X . (G,((((X,K1,G) `) `) `)) is Element of the carrier of X
[G,((((X,K1,G) `) `) `)] is set
{G,((((X,K1,G) `) `) `)} is non empty set
{{G,((((X,K1,G) `) `) `)},{G}} is non empty set
the InternalDiff of X . [G,((((X,K1,G) `) `) `)] is set
RK is V92() V93() integer ext-real set
(X,RK,G) is Element of the carrier of X
RK - 1 is V92() V93() integer ext-real Element of INT
(X,(RK - 1),G) is Element of the carrier of X
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
((G `) `) ` is Element of the carrier of X
(0. X) \ ((G `) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((G `) `)) is Element of the carrier of X
[(0. X),((G `) `)] is set
{(0. X),((G `) `)} is non empty set
{{(0. X),((G `) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((G `) `)] is set
- RK is V92() V93() integer ext-real Element of INT
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
abs (RK - 1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (RK - 1))) is Element of the carrier of X
[(G `),(abs (RK - 1))] is set
{(G `),(abs (RK - 1))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (RK - 1))},{(G `)}} is non empty set
(X) . [(G `),(abs (RK - 1))] is set
- (RK - 1) is V92() V93() integer ext-real Element of INT
(X) . ((G `),(- (RK - 1))) is set
[(G `),(- (RK - 1))] is set
{(G `),(- (RK - 1))} is non empty set
{{(G `),(- (RK - 1))},{(G `)}} is non empty set
(X) . [(G `),(- (RK - 1))] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK1 + 1),(G `)) is Element of the carrier of X
(X) . ((G `),(RK1 + 1)) is set
[(G `),(RK1 + 1)] is set
{(G `),(RK1 + 1)} is non empty set
{{(G `),(RK1 + 1)},{(G `)}} is non empty set
(X) . [(G `),(RK1 + 1)] is set
(X,RK1,(G `)) is Element of the carrier of X
(X) . ((G `),RK1) is set
[(G `),RK1] is set
{(G `),RK1} is non empty set
{{(G `),RK1},{(G `)}} is non empty set
(X) . [(G `),RK1] is set
(X,RK1,(G `)) ` is Element of the carrier of X
(0. X) \ (X,RK1,(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK1,(G `))) is Element of the carrier of X
[(0. X),(X,RK1,(G `))] is set
{(0. X),(X,RK1,(G `))} is non empty set
{{(0. X),(X,RK1,(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK1,(G `))] is set
(G `) \ ((X,RK1,(G `)) `) is Element of the carrier of X
the InternalDiff of X . ((G `),((X,RK1,(G `)) `)) is Element of the carrier of X
[(G `),((X,RK1,(G `)) `)] is set
{(G `),((X,RK1,(G `)) `)} is non empty set
{{(G `),((X,RK1,(G `)) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),((X,RK1,(G `)) `)] is set
- (- RK) is V92() V93() integer ext-real Element of INT
(X,(- (- RK)),G) is Element of the carrier of X
(X,(- (- RK)),G) ` is Element of the carrier of X
(0. X) \ (X,(- (- RK)),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(- (- RK)),G)) is Element of the carrier of X
[(0. X),(X,(- (- RK)),G)] is set
{(0. X),(X,(- (- RK)),G)} is non empty set
{{(0. X),(X,(- (- RK)),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(- (- RK)),G)] is set
(G `) \ ((X,(- (- RK)),G) `) is Element of the carrier of X
the InternalDiff of X . ((G `),((X,(- (- RK)),G) `)) is Element of the carrier of X
[(G `),((X,(- (- RK)),G) `)] is set
{(G `),((X,(- (- RK)),G) `)} is non empty set
{{(G `),((X,(- (- RK)),G) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),((X,(- (- RK)),G) `)] is set
(X,(RK - 1),G) ` is Element of the carrier of X
(0. X) \ (X,(RK - 1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(RK - 1),G)) is Element of the carrier of X
[(0. X),(X,(RK - 1),G)] is set
{(0. X),(X,(RK - 1),G)} is non empty set
{{(0. X),(X,(RK - 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(RK - 1),G)] is set
((X,(RK - 1),G) `) ` is Element of the carrier of X
(0. X) \ ((X,(RK - 1),G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,(RK - 1),G) `)) is Element of the carrier of X
[(0. X),((X,(RK - 1),G) `)] is set
{(0. X),((X,(RK - 1),G) `)} is non empty set
{{(0. X),((X,(RK - 1),G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,(RK - 1),G) `)] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
((X,RK,G) `) ` is Element of the carrier of X
(0. X) \ ((X,RK,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,RK,G) `)) is Element of the carrier of X
[(0. X),((X,RK,G) `)] is set
{(0. X),((X,RK,G) `)} is non empty set
{{(0. X),((X,RK,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,RK,G) `)] is set
((G `) `) \ (((X,RK,G) `) `) is Element of the carrier of X
the InternalDiff of X . (((G `) `),(((X,RK,G) `) `)) is Element of the carrier of X
[((G `) `),(((X,RK,G) `) `)] is set
{((G `) `),(((X,RK,G) `) `)} is non empty set
{((G `) `)} is non empty set
{{((G `) `),(((X,RK,G) `) `)},{((G `) `)}} is non empty set
the InternalDiff of X . [((G `) `),(((X,RK,G) `) `)] is set
(((G `) `) \ (((X,RK,G) `) `)) ` is Element of the carrier of X
(0. X) \ (((G `) `) \ (((X,RK,G) `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(((G `) `) \ (((X,RK,G) `) `))) is Element of the carrier of X
[(0. X),(((G `) `) \ (((X,RK,G) `) `))] is set
{(0. X),(((G `) `) \ (((X,RK,G) `) `))} is non empty set
{{(0. X),(((G `) `) \ (((X,RK,G) `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(((G `) `) \ (((X,RK,G) `) `))] is set
G \ (((X,RK,G) `) `) is Element of the carrier of X
the InternalDiff of X . (G,(((X,RK,G) `) `)) is Element of the carrier of X
[G,(((X,RK,G) `) `)] is set
{G,(((X,RK,G) `) `)} is non empty set
{{G,(((X,RK,G) `) `)},{G}} is non empty set
the InternalDiff of X . [G,(((X,RK,G) `) `)] is set
(G \ (((X,RK,G) `) `)) ` is Element of the carrier of X
(0. X) \ (G \ (((X,RK,G) `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ (((X,RK,G) `) `))) is Element of the carrier of X
[(0. X),(G \ (((X,RK,G) `) `))] is set
{(0. X),(G \ (((X,RK,G) `) `))} is non empty set
{{(0. X),(G \ (((X,RK,G) `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ (((X,RK,G) `) `))] is set
G \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . (G,(X,RK,G)) is Element of the carrier of X
[G,(X,RK,G)] is set
{G,(X,RK,G)} is non empty set
{{G,(X,RK,G)},{G}} is non empty set
the InternalDiff of X . [G,(X,RK,G)] is set
(G \ (X,RK,G)) ` is Element of the carrier of X
(0. X) \ (G \ (X,RK,G)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ (X,RK,G))) is Element of the carrier of X
[(0. X),(G \ (X,RK,G))] is set
{(0. X),(G \ (X,RK,G))} is non empty set
{{(0. X),(G \ (X,RK,G))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ (X,RK,G))] is set
- RK1 is V92() V93() integer ext-real non positive Element of INT
(X,(- RK1),G) is Element of the carrier of X
(X,(- RK1),G) ` is Element of the carrier of X
(0. X) \ (X,(- RK1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(- RK1),G)) is Element of the carrier of X
[(0. X),(X,(- RK1),G)] is set
{(0. X),(X,(- RK1),G)} is non empty set
{{(0. X),(X,(- RK1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(- RK1),G)] is set
(G `) \ ((X,(- RK1),G) `) is Element of the carrier of X
the InternalDiff of X . ((G `),((X,(- RK1),G) `)) is Element of the carrier of X
[(G `),((X,(- RK1),G) `)] is set
{(G `),((X,(- RK1),G) `)} is non empty set
{{(G `),((X,(- RK1),G) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),((X,(- RK1),G) `)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K + 1),G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,(K + 1)) is set
[G,(K + 1)] is set
{G,(K + 1)} is non empty set
{G} is non empty set
{{G,(K + 1)},{G}} is non empty set
(X) . [G,(K + 1)] is set
(X,(K + 1),G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,(K + 1),G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,(K + 1),G)) is Element of the carrier of X
[(0. X),(X,(K + 1),G)] is set
{(0. X),(X,(K + 1),G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,(K + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K + 1),G)] is set
(X,K,G) is Element of the carrier of X
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
((X,K,G) `) \ G is Element of the carrier of X
the InternalDiff of X . (((X,K,G) `),G) is Element of the carrier of X
[((X,K,G) `),G] is set
{((X,K,G) `),G} is non empty set
{((X,K,G) `)} is non empty set
{{((X,K,G) `),G},{((X,K,G) `)}} is non empty set
the InternalDiff of X . [((X,K,G) `),G] is set
G \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,K,G) `)) is Element of the carrier of X
[G,((X,K,G) `)] is set
{G,((X,K,G) `)} is non empty set
{{G,((X,K,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,K,G) `)] is set
(G \ ((X,K,G) `)) ` is Element of the carrier of X
(0. X) \ (G \ ((X,K,G) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ ((X,K,G) `))) is Element of the carrier of X
[(0. X),(G \ ((X,K,G) `))] is set
{(0. X),(G \ ((X,K,G) `))} is non empty set
{{(0. X),(G \ ((X,K,G) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ ((X,K,G) `))] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
((X,K,G) `) ` is Element of the carrier of X
(0. X) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,K,G) `)) is Element of the carrier of X
[(0. X),((X,K,G) `)] is set
{(0. X),((X,K,G) `)} is non empty set
{{(0. X),((X,K,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,K,G) `)] is set
(G `) \ (((X,K,G) `) `) is Element of the carrier of X
the InternalDiff of X . ((G `),(((X,K,G) `) `)) is Element of the carrier of X
[(G `),(((X,K,G) `) `)] is set
{(G `),(((X,K,G) `) `)} is non empty set
{(G `)} is non empty set
{{(G `),(((X,K,G) `) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),(((X,K,G) `) `)] is set
(G `) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((G `),(X,K,G)) is Element of the carrier of X
[(G `),(X,K,G)] is set
{(G `),(X,K,G)} is non empty set
{{(G `),(X,K,G)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),(X,K,G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G is Element of AtomSet X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K + RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K + RK),G) is Element of the carrier of X
(X) . (G,(K + RK)) is set
[G,(K + RK)] is set
{G,(K + RK)} is non empty set
{{G,(K + RK)},{G}} is non empty set
(X) . [G,(K + RK)] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,G) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,RK,G),((X,K,G) `)) is Element of the carrier of X
[(X,RK,G),((X,K,G) `)] is set
{(X,RK,G),((X,K,G) `)} is non empty set
{(X,RK,G)} is non empty set
{{(X,RK,G),((X,K,G) `)},{(X,RK,G)}} is non empty set
the InternalDiff of X . [(X,RK,G),((X,K,G) `)] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
RK1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK1 + 1),G) is Element of the carrier of X
(X) . (G,(RK1 + 1)) is set
[G,(RK1 + 1)] is set
{G,(RK1 + 1)} is non empty set
{{G,(RK1 + 1)},{G}} is non empty set
(X) . [G,(RK1 + 1)] is set
K + RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K + RK1),G) is Element of the carrier of X
(X) . (G,(K + RK1)) is set
[G,(K + RK1)] is set
{G,(K + RK1)} is non empty set
{{G,(K + RK1)},{G}} is non empty set
(X) . [G,(K + RK1)] is set
(X,RK1,G) is Element of the carrier of X
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
(X,RK1,G) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),((X,K,G) `)) is Element of the carrier of X
[(X,RK1,G),((X,K,G) `)] is set
{(X,RK1,G),((X,K,G) `)} is non empty set
{(X,RK1,G)} is non empty set
{{(X,RK1,G),((X,K,G) `)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),((X,K,G) `)] is set
K + (RK1 + 1) is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K + (RK1 + 1)),G) is Element of the carrier of X
(X) . (G,(K + (RK1 + 1))) is set
[G,(K + (RK1 + 1))] is set
{G,(K + (RK1 + 1))} is non empty set
{{G,(K + (RK1 + 1))},{G}} is non empty set
(X) . [G,(K + (RK1 + 1))] is set
(K + RK1) + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,((K + RK1) + 1),G) is Element of the carrier of X
(X) . (G,((K + RK1) + 1)) is set
[G,((K + RK1) + 1)] is set
{G,((K + RK1) + 1)} is non empty set
{{G,((K + RK1) + 1)},{G}} is non empty set
(X) . [G,((K + RK1) + 1)] is set
((X,RK1,G) \ ((X,K,G) `)) ` is Element of the carrier of X
(0. X) \ ((X,RK1,G) \ ((X,K,G) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,RK1,G) \ ((X,K,G) `))) is Element of the carrier of X
[(0. X),((X,RK1,G) \ ((X,K,G) `))] is set
{(0. X),((X,RK1,G) \ ((X,K,G) `))} is non empty set
{{(0. X),((X,RK1,G) \ ((X,K,G) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,RK1,G) \ ((X,K,G) `))] is set
G \ (((X,RK1,G) \ ((X,K,G) `)) `) is Element of the carrier of X
the InternalDiff of X . (G,(((X,RK1,G) \ ((X,K,G) `)) `)) is Element of the carrier of X
[G,(((X,RK1,G) \ ((X,K,G) `)) `)] is set
{G,(((X,RK1,G) \ ((X,K,G) `)) `)} is non empty set
{{G,(((X,RK1,G) \ ((X,K,G) `)) `)},{G}} is non empty set
the InternalDiff of X . [G,(((X,RK1,G) \ ((X,K,G) `)) `)] is set
(X,RK1,G) ` is Element of the carrier of X
(0. X) \ (X,RK1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK1,G)) is Element of the carrier of X
[(0. X),(X,RK1,G)] is set
{(0. X),(X,RK1,G)} is non empty set
{{(0. X),(X,RK1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK1,G)] is set
((X,K,G) `) ` is Element of the carrier of X
(0. X) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,K,G) `)) is Element of the carrier of X
[(0. X),((X,K,G) `)] is set
{(0. X),((X,K,G) `)} is non empty set
{{(0. X),((X,K,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,K,G) `)] is set
((X,RK1,G) `) \ (((X,K,G) `) `) is Element of the carrier of X
the InternalDiff of X . (((X,RK1,G) `),(((X,K,G) `) `)) is Element of the carrier of X
[((X,RK1,G) `),(((X,K,G) `) `)] is set
{((X,RK1,G) `),(((X,K,G) `) `)} is non empty set
{((X,RK1,G) `)} is non empty set
{{((X,RK1,G) `),(((X,K,G) `) `)},{((X,RK1,G) `)}} is non empty set
the InternalDiff of X . [((X,RK1,G) `),(((X,K,G) `) `)] is set
G \ (((X,RK1,G) `) \ (((X,K,G) `) `)) is Element of the carrier of X
the InternalDiff of X . (G,(((X,RK1,G) `) \ (((X,K,G) `) `))) is Element of the carrier of X
[G,(((X,RK1,G) `) \ (((X,K,G) `) `))] is set
{G,(((X,RK1,G) `) \ (((X,K,G) `) `))} is non empty set
{{G,(((X,RK1,G) `) \ (((X,K,G) `) `))},{G}} is non empty set
the InternalDiff of X . [G,(((X,RK1,G) `) \ (((X,K,G) `) `))] is set
K1 is Element of AtomSet X
((X,RK1,G) `) \ K1 is Element of the carrier of X
the InternalDiff of X . (((X,RK1,G) `),K1) is Element of the carrier of X
[((X,RK1,G) `),K1] is set
{((X,RK1,G) `),K1} is non empty set
{{((X,RK1,G) `),K1},{((X,RK1,G) `)}} is non empty set
the InternalDiff of X . [((X,RK1,G) `),K1] is set
G \ (((X,RK1,G) `) \ K1) is Element of the carrier of X
the InternalDiff of X . (G,(((X,RK1,G) `) \ K1)) is Element of the carrier of X
[G,(((X,RK1,G) `) \ K1)] is set
{G,(((X,RK1,G) `) \ K1)} is non empty set
{{G,(((X,RK1,G) `) \ K1)},{G}} is non empty set
the InternalDiff of X . [G,(((X,RK1,G) `) \ K1)] is set
((X,RK1,G) `) \ G is Element of the carrier of X
the InternalDiff of X . (((X,RK1,G) `),G) is Element of the carrier of X
[((X,RK1,G) `),G] is set
{((X,RK1,G) `),G} is non empty set
{{((X,RK1,G) `),G},{((X,RK1,G) `)}} is non empty set
the InternalDiff of X . [((X,RK1,G) `),G] is set
K1 \ (((X,RK1,G) `) \ G) is Element of the carrier of X
the InternalDiff of X . (K1,(((X,RK1,G) `) \ G)) is Element of the carrier of X
[K1,(((X,RK1,G) `) \ G)] is set
{K1,(((X,RK1,G) `) \ G)} is non empty set
{K1} is non empty set
{{K1,(((X,RK1,G) `) \ G)},{K1}} is non empty set
the InternalDiff of X . [K1,(((X,RK1,G) `) \ G)] is set
(X,(RK1 + 1),G) ` is Element of the carrier of X
(0. X) \ (X,(RK1 + 1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(RK1 + 1),G)) is Element of the carrier of X
[(0. X),(X,(RK1 + 1),G)] is set
{(0. X),(X,(RK1 + 1),G)} is non empty set
{{(0. X),(X,(RK1 + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(RK1 + 1),G)] is set
(X,K,G) \ ((X,(RK1 + 1),G) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,(RK1 + 1),G) `)) is Element of the carrier of X
[(X,K,G),((X,(RK1 + 1),G) `)] is set
{(X,K,G),((X,(RK1 + 1),G) `)} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),((X,(RK1 + 1),G) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,(RK1 + 1),G) `)] is set
I is Element of AtomSet X
K1 ` is Element of the carrier of X
(0. X) \ K1 is Element of the carrier of X
the InternalDiff of X . ((0. X),K1) is Element of the carrier of X
[(0. X),K1] is set
{(0. X),K1} is non empty set
{{(0. X),K1},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K1] is set
I \ (K1 `) is Element of the carrier of X
the InternalDiff of X . (I,(K1 `)) is Element of the carrier of X
[I,(K1 `)] is set
{I,(K1 `)} is non empty set
{I} is non empty set
{{I,(K1 `)},{I}} is non empty set
the InternalDiff of X . [I,(K1 `)] is set
(X,(RK1 + 1),G) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,(RK1 + 1),G),((X,K,G) `)) is Element of the carrier of X
[(X,(RK1 + 1),G),((X,K,G) `)] is set
{(X,(RK1 + 1),G),((X,K,G) `)} is non empty set
{(X,(RK1 + 1),G)} is non empty set
{{(X,(RK1 + 1),G),((X,K,G) `)},{(X,(RK1 + 1),G)}} is non empty set
the InternalDiff of X . [(X,(RK1 + 1),G),((X,K,G) `)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) \ ((X,K,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,0,G),((X,K,G) `)) is Element of the carrier of X
[(X,0,G),((X,K,G) `)] is set
{(X,0,G),((X,K,G) `)} is non empty set
{(X,0,G)} is non empty set
{{(X,0,G),((X,K,G) `)},{(X,0,G)}} is non empty set
the InternalDiff of X . [(X,0,G),((X,K,G) `)] is set
K + 0 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K + 0),G) is Element of the carrier of X
(X) . (G,(K + 0)) is set
[G,(K + 0)] is set
{G,(K + 0)} is non empty set
{{G,(K + 0)},{G}} is non empty set
(X) . [G,(K + 0)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G is Element of AtomSet X
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),RK) is set
[(X,K,G),RK] is set
{(X,K,G),RK} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),RK},{(X,K,G)}} is non empty set
(X) . [(X,K,G),RK] is set
K * RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K * RK),G) is Element of the carrier of X
(X) . (G,(K * RK)) is set
[G,(K * RK)] is set
{G,(K * RK)} is non empty set
{{G,(K * RK)},{G}} is non empty set
(X) . [G,(K * RK)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K1,(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),K1) is set
[(X,K,G),K1] is set
{(X,K,G),K1} is non empty set
{{(X,K,G),K1},{(X,K,G)}} is non empty set
(X) . [(X,K,G),K1] is set
K * K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K * K1),G) is Element of the carrier of X
(X) . (G,(K * K1)) is set
[G,(K * K1)] is set
{G,(K * K1)} is non empty set
{{G,(K * K1)},{G}} is non empty set
(X) . [G,(K * K1)] is set
K1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K1 + 1),(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),(K1 + 1)) is set
[(X,K,G),(K1 + 1)] is set
{(X,K,G),(K1 + 1)} is non empty set
{{(X,K,G),(K1 + 1)},{(X,K,G)}} is non empty set
(X) . [(X,K,G),(K1 + 1)] is set
(X,(K * K1),G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,(K * K1),G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,(K * K1),G)) is Element of the carrier of X
[(0. X),(X,(K * K1),G)] is set
{(0. X),(X,(K * K1),G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,(K * K1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K * K1),G)] is set
(X,K,G) \ ((X,(K * K1),G) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,(K * K1),G) `)) is Element of the carrier of X
[(X,K,G),((X,(K * K1),G) `)] is set
{(X,K,G),((X,(K * K1),G) `)} is non empty set
{{(X,K,G),((X,(K * K1),G) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,(K * K1),G) `)] is set
K + (K * K1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K + (K * K1)),G) is Element of the carrier of X
(X) . (G,(K + (K * K1))) is set
[G,(K + (K * K1))] is set
{G,(K + (K * K1))} is non empty set
{{G,(K + (K * K1))},{G}} is non empty set
(X) . [G,(K + (K * K1))] is set
K * (K1 + 1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K * (K1 + 1)),G) is Element of the carrier of X
(X) . (G,(K * (K1 + 1))) is set
[G,(K * (K1 + 1))] is set
{G,(K * (K1 + 1))} is non empty set
{{G,(K * (K1 + 1))},{G}} is non empty set
(X) . [G,(K * (K1 + 1))] is set
(X,0,(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),0) is set
[(X,K,G),0] is set
{(X,K,G),0} is non empty set
{{(X,K,G),0},{(X,K,G)}} is non empty set
(X) . [(X,K,G),0] is set
K * 0 is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative Element of NAT
(X,(K * 0),G) is Element of the carrier of X
(X) . (G,(K * 0)) is set
[G,(K * 0)] is set
{G,(K * 0)} is non empty set
{{G,(K * 0)},{G}} is non empty set
(X) . [G,(K * 0)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is Element of AtomSet X
G \ K is Element of AtomSet X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (G,K) is Element of the carrier of X
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
the InternalDiff of X . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,(G \ K)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G \ K),RK) is set
[(G \ K),RK] is set
{(G \ K),RK} is non empty set
{(G \ K)} is non empty set
{{(G \ K),RK},{(G \ K)}} is non empty set
(X) . [(G \ K),RK] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,K) is Element of the carrier of X
(X) . (K,RK) is set
[K,RK] is set
{K,RK} is non empty set
{K} is non empty set
{{K,RK},{K}} is non empty set
(X) . [K,RK] is set
(X,RK,G) \ (X,RK,K) is Element of the carrier of X
the InternalDiff of X . ((X,RK,G),(X,RK,K)) is Element of the carrier of X
[(X,RK,G),(X,RK,K)] is set
{(X,RK,G),(X,RK,K)} is non empty set
{(X,RK,G)} is non empty set
{{(X,RK,G),(X,RK,K)},{(X,RK,G)}} is non empty set
the InternalDiff of X . [(X,RK,G),(X,RK,K)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K1,K) is Element of the carrier of X
(X) . (K,K1) is set
[K,K1] is set
{K,K1} is non empty set
{{K,K1},{K}} is non empty set
(X) . [K,K1] is set
(X,K1,K) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,K1,K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,K)) is Element of the carrier of X
[(0. X),(X,K1,K)] is set
{(0. X),(X,K1,K)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,K1,K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,K)] is set
K1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K1 + 1),G) is Element of the carrier of X
(X) . (G,(K1 + 1)) is set
[G,(K1 + 1)] is set
{G,(K1 + 1)} is non empty set
{{G,(K1 + 1)},{G}} is non empty set
(X) . [G,(K1 + 1)] is set
(X,K1,(G \ K)) is Element of the carrier of X
(X) . ((G \ K),K1) is set
[(G \ K),K1] is set
{(G \ K),K1} is non empty set
{{(G \ K),K1},{(G \ K)}} is non empty set
(X) . [(G \ K),K1] is set
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,K1,G) \ (X,K1,K) is Element of the carrier of X
the InternalDiff of X . ((X,K1,G),(X,K1,K)) is Element of the carrier of X
[(X,K1,G),(X,K1,K)] is set
{(X,K1,G),(X,K1,K)} is non empty set
{(X,K1,G)} is non empty set
{{(X,K1,G),(X,K1,K)},{(X,K1,G)}} is non empty set
the InternalDiff of X . [(X,K1,G),(X,K1,K)] is set
(X,(K1 + 1),(G \ K)) is Element of the carrier of X
(X) . ((G \ K),(K1 + 1)) is set
[(G \ K),(K1 + 1)] is set
{(G \ K),(K1 + 1)} is non empty set
{{(G \ K),(K1 + 1)},{(G \ K)}} is non empty set
(X) . [(G \ K),(K1 + 1)] is set
((X,K1,G) \ (X,K1,K)) ` is Element of the carrier of X
(0. X) \ ((X,K1,G) \ (X,K1,K)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,K1,G) \ (X,K1,K))) is Element of the carrier of X
[(0. X),((X,K1,G) \ (X,K1,K))] is set
{(0. X),((X,K1,G) \ (X,K1,K))} is non empty set
{{(0. X),((X,K1,G) \ (X,K1,K))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,K1,G) \ (X,K1,K))] is set
(G \ K) \ (((X,K1,G) \ (X,K1,K)) `) is Element of the carrier of X
the InternalDiff of X . ((G \ K),(((X,K1,G) \ (X,K1,K)) `)) is Element of the carrier of X
[(G \ K),(((X,K1,G) \ (X,K1,K)) `)] is set
{(G \ K),(((X,K1,G) \ (X,K1,K)) `)} is non empty set
{{(G \ K),(((X,K1,G) \ (X,K1,K)) `)},{(G \ K)}} is non empty set
the InternalDiff of X . [(G \ K),(((X,K1,G) \ (X,K1,K)) `)] is set
G \ (((X,K1,G) \ (X,K1,K)) `) is Element of the carrier of X
the InternalDiff of X . (G,(((X,K1,G) \ (X,K1,K)) `)) is Element of the carrier of X
[G,(((X,K1,G) \ (X,K1,K)) `)] is set
{G,(((X,K1,G) \ (X,K1,K)) `)} is non empty set
{{G,(((X,K1,G) \ (X,K1,K)) `)},{G}} is non empty set
the InternalDiff of X . [G,(((X,K1,G) \ (X,K1,K)) `)] is set
(G \ (((X,K1,G) \ (X,K1,K)) `)) \ K is Element of the carrier of X
the InternalDiff of X . ((G \ (((X,K1,G) \ (X,K1,K)) `)),K) is Element of the carrier of X
[(G \ (((X,K1,G) \ (X,K1,K)) `)),K] is set
{(G \ (((X,K1,G) \ (X,K1,K)) `)),K} is non empty set
{(G \ (((X,K1,G) \ (X,K1,K)) `))} is non empty set
{{(G \ (((X,K1,G) \ (X,K1,K)) `)),K},{(G \ (((X,K1,G) \ (X,K1,K)) `))}} is non empty set
the InternalDiff of X . [(G \ (((X,K1,G) \ (X,K1,K)) `)),K] is set
(X,K1,G) ` is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
((X,K1,G) `) \ ((X,K1,K) `) is Element of the carrier of X
the InternalDiff of X . (((X,K1,G) `),((X,K1,K) `)) is Element of the carrier of X
[((X,K1,G) `),((X,K1,K) `)] is set
{((X,K1,G) `),((X,K1,K) `)} is non empty set
{((X,K1,G) `)} is non empty set
{{((X,K1,G) `),((X,K1,K) `)},{((X,K1,G) `)}} is non empty set
the InternalDiff of X . [((X,K1,G) `),((X,K1,K) `)] is set
G \ (((X,K1,G) `) \ ((X,K1,K) `)) is Element of the carrier of X
the InternalDiff of X . (G,(((X,K1,G) `) \ ((X,K1,K) `))) is Element of the carrier of X
[G,(((X,K1,G) `) \ ((X,K1,K) `))] is set
{G,(((X,K1,G) `) \ ((X,K1,K) `))} is non empty set
{{G,(((X,K1,G) `) \ ((X,K1,K) `))},{G}} is non empty set
the InternalDiff of X . [G,(((X,K1,G) `) \ ((X,K1,K) `))] is set
(G \ (((X,K1,G) `) \ ((X,K1,K) `))) \ K is Element of the carrier of X
the InternalDiff of X . ((G \ (((X,K1,G) `) \ ((X,K1,K) `))),K) is Element of the carrier of X
[(G \ (((X,K1,G) `) \ ((X,K1,K) `))),K] is set
{(G \ (((X,K1,G) `) \ ((X,K1,K) `))),K} is non empty set
{(G \ (((X,K1,G) `) \ ((X,K1,K) `)))} is non empty set
{{(G \ (((X,K1,G) `) \ ((X,K1,K) `))),K},{(G \ (((X,K1,G) `) \ ((X,K1,K) `)))}} is non empty set
the InternalDiff of X . [(G \ (((X,K1,G) `) \ ((X,K1,K) `))),K] is set
((X,K1,G) `) \ G is Element of the carrier of X
the InternalDiff of X . (((X,K1,G) `),G) is Element of the carrier of X
[((X,K1,G) `),G] is set
{((X,K1,G) `),G} is non empty set
{{((X,K1,G) `),G},{((X,K1,G) `)}} is non empty set
the InternalDiff of X . [((X,K1,G) `),G] is set
((X,K1,K) `) \ (((X,K1,G) `) \ G) is Element of the carrier of X
the InternalDiff of X . (((X,K1,K) `),(((X,K1,G) `) \ G)) is Element of the carrier of X
[((X,K1,K) `),(((X,K1,G) `) \ G)] is set
{((X,K1,K) `),(((X,K1,G) `) \ G)} is non empty set
{((X,K1,K) `)} is non empty set
{{((X,K1,K) `),(((X,K1,G) `) \ G)},{((X,K1,K) `)}} is non empty set
the InternalDiff of X . [((X,K1,K) `),(((X,K1,G) `) \ G)] is set
(((X,K1,K) `) \ (((X,K1,G) `) \ G)) \ K is Element of the carrier of X
the InternalDiff of X . ((((X,K1,K) `) \ (((X,K1,G) `) \ G)),K) is Element of the carrier of X
[(((X,K1,K) `) \ (((X,K1,G) `) \ G)),K] is set
{(((X,K1,K) `) \ (((X,K1,G) `) \ G)),K} is non empty set
{(((X,K1,K) `) \ (((X,K1,G) `) \ G))} is non empty set
{{(((X,K1,K) `) \ (((X,K1,G) `) \ G)),K},{(((X,K1,K) `) \ (((X,K1,G) `) \ G))}} is non empty set
the InternalDiff of X . [(((X,K1,K) `) \ (((X,K1,G) `) \ G)),K] is set
((X,K1,K) `) \ K is Element of the carrier of X
the InternalDiff of X . (((X,K1,K) `),K) is Element of the carrier of X
[((X,K1,K) `),K] is set
{((X,K1,K) `),K} is non empty set
{{((X,K1,K) `),K},{((X,K1,K) `)}} is non empty set
the InternalDiff of X . [((X,K1,K) `),K] is set
(((X,K1,K) `) \ K) \ (((X,K1,G) `) \ G) is Element of the carrier of X
the InternalDiff of X . ((((X,K1,K) `) \ K),(((X,K1,G) `) \ G)) is Element of the carrier of X
[(((X,K1,K) `) \ K),(((X,K1,G) `) \ G)] is set
{(((X,K1,K) `) \ K),(((X,K1,G) `) \ G)} is non empty set
{(((X,K1,K) `) \ K)} is non empty set
{{(((X,K1,K) `) \ K),(((X,K1,G) `) \ G)},{(((X,K1,K) `) \ K)}} is non empty set
the InternalDiff of X . [(((X,K1,K) `) \ K),(((X,K1,G) `) \ G)] is set
(X,(K1 + 1),K) is Element of the carrier of X
(X) . (K,(K1 + 1)) is set
[K,(K1 + 1)] is set
{K,(K1 + 1)} is non empty set
{{K,(K1 + 1)},{K}} is non empty set
(X) . [K,(K1 + 1)] is set
(X,(K1 + 1),K) ` is Element of the carrier of X
(0. X) \ (X,(K1 + 1),K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(K1 + 1),K)) is Element of the carrier of X
[(0. X),(X,(K1 + 1),K)] is set
{(0. X),(X,(K1 + 1),K)} is non empty set
{{(0. X),(X,(K1 + 1),K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K1 + 1),K)] is set
((X,(K1 + 1),K) `) \ (((X,K1,G) `) \ G) is Element of the carrier of X
the InternalDiff of X . (((X,(K1 + 1),K) `),(((X,K1,G) `) \ G)) is Element of the carrier of X
[((X,(K1 + 1),K) `),(((X,K1,G) `) \ G)] is set
{((X,(K1 + 1),K) `),(((X,K1,G) `) \ G)} is non empty set
{((X,(K1 + 1),K) `)} is non empty set
{{((X,(K1 + 1),K) `),(((X,K1,G) `) \ G)},{((X,(K1 + 1),K) `)}} is non empty set
the InternalDiff of X . [((X,(K1 + 1),K) `),(((X,K1,G) `) \ G)] is set
(X,(K1 + 1),G) ` is Element of the carrier of X
(0. X) \ (X,(K1 + 1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(K1 + 1),G)) is Element of the carrier of X
[(0. X),(X,(K1 + 1),G)] is set
{(0. X),(X,(K1 + 1),G)} is non empty set
{{(0. X),(X,(K1 + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K1 + 1),G)] is set
((X,(K1 + 1),K) `) \ ((X,(K1 + 1),G) `) is Element of the carrier of X
the InternalDiff of X . (((X,(K1 + 1),K) `),((X,(K1 + 1),G) `)) is Element of the carrier of X
[((X,(K1 + 1),K) `),((X,(K1 + 1),G) `)] is set
{((X,(K1 + 1),K) `),((X,(K1 + 1),G) `)} is non empty set
{{((X,(K1 + 1),K) `),((X,(K1 + 1),G) `)},{((X,(K1 + 1),K) `)}} is non empty set
the InternalDiff of X . [((X,(K1 + 1),K) `),((X,(K1 + 1),G) `)] is set
(X,(K1 + 1),K) \ (X,(K1 + 1),G) is Element of the carrier of X
the InternalDiff of X . ((X,(K1 + 1),K),(X,(K1 + 1),G)) is Element of the carrier of X
[(X,(K1 + 1),K),(X,(K1 + 1),G)] is set
{(X,(K1 + 1),K),(X,(K1 + 1),G)} is non empty set
{(X,(K1 + 1),K)} is non empty set
{{(X,(K1 + 1),K),(X,(K1 + 1),G)},{(X,(K1 + 1),K)}} is non empty set
the InternalDiff of X . [(X,(K1 + 1),K),(X,(K1 + 1),G)] is set
((X,(K1 + 1),K) \ (X,(K1 + 1),G)) ` is Element of the carrier of X
(0. X) \ ((X,(K1 + 1),K) \ (X,(K1 + 1),G)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,(K1 + 1),K) \ (X,(K1 + 1),G))) is Element of the carrier of X
[(0. X),((X,(K1 + 1),K) \ (X,(K1 + 1),G))] is set
{(0. X),((X,(K1 + 1),K) \ (X,(K1 + 1),G))} is non empty set
{{(0. X),((X,(K1 + 1),K) \ (X,(K1 + 1),G))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,(K1 + 1),K) \ (X,(K1 + 1),G))] is set
(X,(K1 + 1),G) \ (X,(K1 + 1),K) is Element of the carrier of X
the InternalDiff of X . ((X,(K1 + 1),G),(X,(K1 + 1),K)) is Element of the carrier of X
[(X,(K1 + 1),G),(X,(K1 + 1),K)] is set
{(X,(K1 + 1),G),(X,(K1 + 1),K)} is non empty set
{(X,(K1 + 1),G)} is non empty set
{{(X,(K1 + 1),G),(X,(K1 + 1),K)},{(X,(K1 + 1),G)}} is non empty set
the InternalDiff of X . [(X,(K1 + 1),G),(X,(K1 + 1),K)] is set
(X,0,(G \ K)) is Element of the carrier of X
(X) . ((G \ K),0) is set
[(G \ K),0] is set
{(G \ K),0} is non empty set
{{(G \ K),0},{(G \ K)}} is non empty set
(X) . [(G \ K),0] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((X,0,G),(0. X)) is Element of the carrier of X
[(X,0,G),(0. X)] is set
{(X,0,G),(0. X)} is non empty set
{(X,0,G)} is non empty set
{{(X,0,G),(0. X)},{(X,0,G)}} is non empty set
the InternalDiff of X . [(X,0,G),(0. X)] is set
(X,0,K) is Element of the carrier of X
(X) . (K,0) is set
[K,0] is set
{K,0} is non empty set
{{K,0},{K}} is non empty set
(X) . [K,0] is set
(X,0,G) \ (X,0,K) is Element of the carrier of X
the InternalDiff of X . ((X,0,G),(X,0,K)) is Element of the carrier of X
[(X,0,G),(X,0,K)] is set
{(X,0,G),(X,0,K)} is non empty set
{{(X,0,G),(X,0,K)},{(X,0,G)}} is non empty set
the InternalDiff of X . [(X,0,G),(X,0,K)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is Element of AtomSet X
G \ K is Element of AtomSet X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (G,K) is Element of the carrier of X
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
the InternalDiff of X . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- RK is V92() V93() integer ext-real non positive Element of INT
(X,(- RK),(G \ K)) is Element of the carrier of X
(X,(- RK),G) is Element of the carrier of X
(X,(- RK),K) is Element of the carrier of X
(X,(- RK),G) \ (X,(- RK),K) is Element of the carrier of X
the InternalDiff of X . ((X,(- RK),G),(X,(- RK),K)) is Element of the carrier of X
[(X,(- RK),G),(X,(- RK),K)] is set
{(X,(- RK),G),(X,(- RK),K)} is non empty set
{(X,(- RK),G)} is non empty set
{{(X,(- RK),G),(X,(- RK),K)},{(X,(- RK),G)}} is non empty set
the InternalDiff of X . [(X,(- RK),G),(X,(- RK),K)] is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K ` is Element of the carrier of X
(0. X) \ K is Element of the carrier of X
the InternalDiff of X . ((0. X),K) is Element of the carrier of X
[(0. X),K] is set
{(0. X),K} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K] is set
I is Element of AtomSet X
(X,RK,I) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (I,RK) is set
[I,RK] is set
{I,RK} is non empty set
{I} is non empty set
{{I,RK},{I}} is non empty set
(X) . [I,RK] is set
RI is Element of AtomSet X
(X,RK,RI) is Element of the carrier of X
(X) . (RI,RK) is set
[RI,RK] is set
{RI,RK} is non empty set
{RI} is non empty set
{{RI,RK},{RI}} is non empty set
(X) . [RI,RK] is set
(G \ K) ` is Element of the carrier of X
(0. X) \ (G \ K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ K)) is Element of the carrier of X
[(0. X),(G \ K)] is set
{(0. X),(G \ K)} is non empty set
{{(0. X),(G \ K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ K)] is set
(X,RK,((G \ K) `)) is Element of the carrier of X
(X) . (((G \ K) `),RK) is set
[((G \ K) `),RK] is set
{((G \ K) `),RK} is non empty set
{((G \ K) `)} is non empty set
{{((G \ K) `),RK},{((G \ K) `)}} is non empty set
(X) . [((G \ K) `),RK] is set
(G `) \ (K `) is Element of the carrier of X
the InternalDiff of X . ((G `),(K `)) is Element of the carrier of X
[(G `),(K `)] is set
{(G `),(K `)} is non empty set
{(G `)} is non empty set
{{(G `),(K `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),(K `)] is set
(X,RK,((G `) \ (K `))) is Element of the carrier of X
(X) . (((G `) \ (K `)),RK) is set
[((G `) \ (K `)),RK] is set
{((G `) \ (K `)),RK} is non empty set
{((G `) \ (K `))} is non empty set
{{((G `) \ (K `)),RK},{((G `) \ (K `))}} is non empty set
(X) . [((G `) \ (K `)),RK] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),K) is set
[(G `),K] is set
{(G `),K} is non empty set
{(G `)} is non empty set
{{(G `),K},{(G `)}} is non empty set
(X) . [(G `),K] is set
(X,K,G) is Element of the carrier of X
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,(G `)) is Element of the carrier of X
(X) . ((G `),RK) is set
[(G `),RK] is set
{(G `),RK} is non empty set
{{(G `),RK},{(G `)}} is non empty set
(X) . [(G `),RK] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK + 1),(G `)) is Element of the carrier of X
(X) . ((G `),(RK + 1)) is set
[(G `),(RK + 1)] is set
{(G `),(RK + 1)} is non empty set
{{(G `),(RK + 1)},{(G `)}} is non empty set
(X) . [(G `),(RK + 1)] is set
(X,(RK + 1),(0. X)) is Element of the carrier of X
(X) . ((0. X),(RK + 1)) is set
[(0. X),(RK + 1)] is set
{(0. X),(RK + 1)} is non empty set
{{(0. X),(RK + 1)},{(0. X)}} is non empty set
(X) . [(0. X),(RK + 1)] is set
(X,(RK + 1),G) is Element of the carrier of X
(X) . (G,(RK + 1)) is set
[G,(RK + 1)] is set
{G,(RK + 1)} is non empty set
{{G,(RK + 1)},{G}} is non empty set
(X) . [G,(RK + 1)] is set
(X,(RK + 1),(0. X)) \ (X,(RK + 1),G) is Element of the carrier of X
the InternalDiff of X . ((X,(RK + 1),(0. X)),(X,(RK + 1),G)) is Element of the carrier of X
[(X,(RK + 1),(0. X)),(X,(RK + 1),G)] is set
{(X,(RK + 1),(0. X)),(X,(RK + 1),G)} is non empty set
{(X,(RK + 1),(0. X))} is non empty set
{{(X,(RK + 1),(0. X)),(X,(RK + 1),G)},{(X,(RK + 1),(0. X))}} is non empty set
the InternalDiff of X . [(X,(RK + 1),(0. X)),(X,(RK + 1),G)] is set
(X,(RK + 1),G) ` is Element of the carrier of X
(0. X) \ (X,(RK + 1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(RK + 1),G)) is Element of the carrier of X
[(0. X),(X,(RK + 1),G)] is set
{(0. X),(X,(RK + 1),G)} is non empty set
{{(0. X),(X,(RK + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(RK + 1),G)] is set
(X,0,(G `)) is Element of the carrier of X
(X) . ((G `),0) is set
[(G `),0] is set
{(G `),0} is non empty set
{{(G `),0},{(G `)}} is non empty set
(X) . [(G `),0] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) ` is Element of the carrier of X
(0. X) \ (X,0,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,0,G)) is Element of the carrier of X
[(0. X),(X,0,G)] is set
{(0. X),(X,0,G)} is non empty set
{{(0. X),(X,0,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,0,G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),K) is set
[(G `),K] is set
{(G `),K} is non empty set
{(G `)} is non empty set
{{(G `),K},{(G `)}} is non empty set
(X) . [(G `),K] is set
(X,K,G) is Element of the carrier of X
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,(G `)) is Element of the carrier of X
(X) . ((G `),RK) is set
[(G `),RK] is set
{(G `),RK} is non empty set
{{(G `),RK},{(G `)}} is non empty set
(X) . [(G `),RK] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
RK + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(RK + 1),(G `)) is Element of the carrier of X
(X) . ((G `),(RK + 1)) is set
[(G `),(RK + 1)] is set
{(G `),(RK + 1)} is non empty set
{{(G `),(RK + 1)},{(G `)}} is non empty set
(X) . [(G `),(RK + 1)] is set
((X,RK,G) `) ` is Element of the carrier of X
(0. X) \ ((X,RK,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,RK,G) `)) is Element of the carrier of X
[(0. X),((X,RK,G) `)] is set
{(0. X),((X,RK,G) `)} is non empty set
{{(0. X),((X,RK,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,RK,G) `)] is set
(G `) \ (((X,RK,G) `) `) is Element of the carrier of X
the InternalDiff of X . ((G `),(((X,RK,G) `) `)) is Element of the carrier of X
[(G `),(((X,RK,G) `) `)] is set
{(G `),(((X,RK,G) `) `)} is non empty set
{{(G `),(((X,RK,G) `) `)},{(G `)}} is non empty set
the InternalDiff of X . [(G `),(((X,RK,G) `) `)] is set
G \ ((X,RK,G) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,RK,G) `)) is Element of the carrier of X
[G,((X,RK,G) `)] is set
{G,((X,RK,G) `)} is non empty set
{{G,((X,RK,G) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,RK,G) `)] is set
(G \ ((X,RK,G) `)) ` is Element of the carrier of X
(0. X) \ (G \ ((X,RK,G) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G \ ((X,RK,G) `))) is Element of the carrier of X
[(0. X),(G \ ((X,RK,G) `))] is set
{(0. X),(G \ ((X,RK,G) `))} is non empty set
{{(0. X),(G \ ((X,RK,G) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G \ ((X,RK,G) `))] is set
(X,(RK + 1),G) is Element of the carrier of X
(X) . (G,(RK + 1)) is set
[G,(RK + 1)] is set
{G,(RK + 1)} is non empty set
{{G,(RK + 1)},{G}} is non empty set
(X) . [G,(RK + 1)] is set
(X,(RK + 1),G) ` is Element of the carrier of X
(0. X) \ (X,(RK + 1),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(RK + 1),G)) is Element of the carrier of X
[(0. X),(X,(RK + 1),G)] is set
{(0. X),(X,(RK + 1),G)} is non empty set
{{(0. X),(X,(RK + 1),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(RK + 1),G)] is set
(X,0,(G `)) is Element of the carrier of X
(X) . ((G `),0) is set
[(G `),0] is set
{(G `),0} is non empty set
{{(G `),0},{(G `)}} is non empty set
(X) . [(G `),0] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) ` is Element of the carrier of X
(0. X) \ (X,0,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,0,G)) is Element of the carrier of X
[(0. X),(X,0,G)] is set
{(0. X),(X,0,G)} is non empty set
{{(0. X),(X,0,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,0,G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G is Element of AtomSet X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
- K is V92() V93() integer ext-real non positive Element of INT
(X,(- K),(G `)) is Element of the carrier of X
(X,(- K),G) is Element of the carrier of X
(X,(- K),G) ` is Element of the carrier of X
(0. X) \ (X,(- K),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(- K),G)) is Element of the carrier of X
[(0. X),(X,(- K),G)] is set
{(0. X),(X,(- K),G)} is non empty set
{{(0. X),(X,(- K),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(- K),G)] is set
RK is Element of AtomSet X
(X,(- K),RK) is Element of the carrier of X
RK ` is Element of the carrier of X
(0. X) \ RK is Element of the carrier of X
the InternalDiff of X . ((0. X),RK) is Element of the carrier of X
[(0. X),RK] is set
{(0. X),RK} is non empty set
{{(0. X),RK},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),RK] is set
(X,K,(RK `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((RK `),K) is set
[(RK `),K] is set
{(RK `),K} is non empty set
{(RK `)} is non empty set
{{(RK `),K},{(RK `)}} is non empty set
(X) . [(RK `),K] is set
(X,K,RK) is Element of the carrier of X
(X) . (RK,K) is set
[RK,K] is set
{RK,K} is non empty set
{RK} is non empty set
{{RK,K},{RK}} is non empty set
(X) . [RK,K] is set
(X,K,RK) ` is Element of the carrier of X
(0. X) \ (X,K,RK) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,RK)) is Element of the carrier of X
[(0. X),(X,K,RK)] is set
{(0. X),(X,K,RK)} is non empty set
{{(0. X),(X,K,RK)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,RK)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
K is Element of AtomSet X
BranchV K is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K <= b₁ } is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,((G `) `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (((G `) `),RK) is set
[((G `) `),RK] is set
{((G `) `),RK} is non empty set
{((G `) `)} is non empty set
{{((G `) `),RK},{((G `) `)}} is non empty set
(X) . [((G `) `),RK] is set
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{G} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K1,((G `) `)) is Element of the carrier of X
(X) . (((G `) `),K1) is set
[((G `) `),K1] is set
{((G `) `),K1} is non empty set
{{((G `) `),K1},{((G `) `)}} is non empty set
(X) . [((G `) `),K1] is set
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
I is Element of AtomSet X
K1 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
(X,(K1 + 1),((G `) `)) is Element of the carrier of X
(X) . (((G `) `),(K1 + 1)) is set
[((G `) `),(K1 + 1)] is set
{((G `) `),(K1 + 1)} is non empty set
{{((G `) `),(K1 + 1)},{((G `) `)}} is non empty set
(X) . [((G `) `),(K1 + 1)] is set
RI is Element of AtomSet X
BranchV RI is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : RI <= b₁ } is set
(X,K1,G) ` is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
(X,K1,((G `) `)) ` is Element of the carrier of X
(0. X) \ (X,K1,((G `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,((G `) `))) is Element of the carrier of X
[(0. X),(X,K1,((G `) `))] is set
{(0. X),(X,K1,((G `) `))} is non empty set
{{(0. X),(X,K1,((G `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,((G `) `))] is set
(X,(K1 + 1),G) is Element of the carrier of X
(X) . (G,(K1 + 1)) is set
[G,(K1 + 1)] is set
{G,(K1 + 1)} is non empty set
{{G,(K1 + 1)},{G}} is non empty set
(X) . [G,(K1 + 1)] is set
G \ ((X,K1,((G `) `)) `) is Element of the carrier of X
the InternalDiff of X . (G,((X,K1,((G `) `)) `)) is Element of the carrier of X
[G,((X,K1,((G `) `)) `)] is set
{G,((X,K1,((G `) `)) `)} is non empty set
{{G,((X,K1,((G `) `)) `)},{G}} is non empty set
the InternalDiff of X . [G,((X,K1,((G `) `)) `)] is set
((G `) `) \ ((X,K1,((G `) `)) `) is Element of the carrier of X
the InternalDiff of X . (((G `) `),((X,K1,((G `) `)) `)) is Element of the carrier of X
[((G `) `),((X,K1,((G `) `)) `)] is set
{((G `) `),((X,K1,((G `) `)) `)} is non empty set
{{((G `) `),((X,K1,((G `) `)) `)},{((G `) `)}} is non empty set
the InternalDiff of X . [((G `) `),((X,K1,((G `) `)) `)] is set
(((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `)) is Element of the carrier of X
the InternalDiff of X . ((((G `) `) \ ((X,K1,((G `) `)) `)),(G \ ((X,K1,((G `) `)) `))) is Element of the carrier of X
[(((G `) `) \ ((X,K1,((G `) `)) `)),(G \ ((X,K1,((G `) `)) `))] is set
{(((G `) `) \ ((X,K1,((G `) `)) `)),(G \ ((X,K1,((G `) `)) `))} is non empty set
{(((G `) `) \ ((X,K1,((G `) `)) `))} is non empty set
{{(((G `) `) \ ((X,K1,((G `) `)) `)),(G \ ((X,K1,((G `) `)) `))},{(((G `) `) \ ((X,K1,((G `) `)) `))}} is non empty set
the InternalDiff of X . [(((G `) `) \ ((X,K1,((G `) `)) `)),(G \ ((X,K1,((G `) `)) `))] is set
((G `) `) \ G is Element of the carrier of X
the InternalDiff of X . (((G `) `),G) is Element of the carrier of X
[((G `) `),G] is set
{((G `) `),G} is non empty set
{{((G `) `),G},{((G `) `)}} is non empty set
the InternalDiff of X . [((G `) `),G] is set
((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))) \ (((G `) `) \ G) is Element of the carrier of X
the InternalDiff of X . (((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))),(((G `) `) \ G)) is Element of the carrier of X
[((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))),(((G `) `) \ G)] is set
{((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))),(((G `) `) \ G)} is non empty set
{((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `)))} is non empty set
{{((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))),(((G `) `) \ G)},{((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `)))}} is non empty set
the InternalDiff of X . [((((G `) `) \ ((X,K1,((G `) `)) `)) \ (G \ ((X,K1,((G `) `)) `))),(((G `) `) \ G)] is set
(X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G) is Element of the carrier of X
the InternalDiff of X . ((X,(K1 + 1),((G `) `)),(X,(K1 + 1),G)) is Element of the carrier of X
[(X,(K1 + 1),((G `) `)),(X,(K1 + 1),G)] is set
{(X,(K1 + 1),((G `) `)),(X,(K1 + 1),G)} is non empty set
{(X,(K1 + 1),((G `) `))} is non empty set
{{(X,(K1 + 1),((G `) `)),(X,(K1 + 1),G)},{(X,(K1 + 1),((G `) `))}} is non empty set
the InternalDiff of X . [(X,(K1 + 1),((G `) `)),(X,(K1 + 1),G)] is set
((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)) \ (((G `) `) \ G) is Element of the carrier of X
the InternalDiff of X . (((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(((G `) `) \ G)) is Element of the carrier of X
[((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(((G `) `) \ G)] is set
{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(((G `) `) \ G)} is non empty set
{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G))} is non empty set
{{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(((G `) `) \ G)},{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G))}} is non empty set
the InternalDiff of X . [((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(((G `) `) \ G)] is set
((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)) \ (0. X) is Element of the carrier of X
the InternalDiff of X . (((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(0. X)) is Element of the carrier of X
[((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(0. X)] is set
{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(0. X)} is non empty set
{{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(0. X)},{((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G))}} is non empty set
the InternalDiff of X . [((X,(K1 + 1),((G `) `)) \ (X,(K1 + 1),G)),(0. X)] is set
BranchV I is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : I <= b₁ } is set
RK1 is Element of AtomSet X
BranchV RK1 is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : RK1 <= b₁ } is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(0. X) \ (X,0,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,0,G)) is Element of the carrier of X
[(0. X),(X,0,G)] is set
{(0. X),(X,0,G)} is non empty set
{{(0. X),(X,0,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,0,G)] is set
(X,0,((G `) `)) is Element of the carrier of X
(X) . (((G `) `),0) is set
[((G `) `),0] is set
{((G `) `),0} is non empty set
{{((G `) `),0},{((G `) `)}} is non empty set
(X) . [((G `) `),0] is set
K1 is Element of AtomSet X
BranchV K1 is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K1 <= b₁ } is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
(X,K,((G `) `)) is Element of the carrier of X
(X) . (((G `) `),K) is set
[((G `) `),K] is set
{((G `) `),K} is non empty set
{((G `) `)} is non empty set
{{((G `) `),K},{((G `) `)}} is non empty set
(X) . [((G `) `),K] is set
(X,K,((G `) `)) ` is Element of the carrier of X
(0. X) \ (X,K,((G `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,((G `) `))) is Element of the carrier of X
[(0. X),(X,K,((G `) `))] is set
{(0. X),(X,K,((G `) `))} is non empty set
{{(0. X),(X,K,((G `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,((G `) `))] is set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
K1 is Element of AtomSet X
BranchV K1 is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K1 <= b₁ } is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is V92() V93() integer ext-real set
(X,K,G) is Element of the carrier of X
RK is V92() V93() integer ext-real set
(X,RK,G) is Element of the carrier of X
(X,K,G) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((X,K,G),(X,RK,G)) is Element of the carrier of X
[(X,K,G),(X,RK,G)] is set
{(X,K,G),(X,RK,G)} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),(X,RK,G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,RK,G)] is set
K - RK is V92() V93() integer ext-real Element of INT
(X,(K - RK),G) is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K - RK1 is V92() V93() integer ext-real Element of INT
(K - RK1) + RK1 is V92() V93() integer ext-real Element of INT
(X,((K - RK1) + RK1),G) is Element of the carrier of X
(X,RK1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{G} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,G) is Element of the carrier of X
(X) . (G,I) is set
[G,I] is set
{G,I} is non empty set
{{G,I},{G}} is non empty set
(X) . [G,I] is set
(X,I,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,I,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,I,G)) is Element of the carrier of X
[(0. X),(X,I,G)] is set
{(0. X),(X,I,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,I,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,I,G)] is set
(X,RK1,G) \ ((X,I,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),((X,I,G) `)) is Element of the carrier of X
[(X,RK1,G),((X,I,G) `)] is set
{(X,RK1,G),((X,I,G) `)} is non empty set
{(X,RK1,G)} is non empty set
{{(X,RK1,G),((X,I,G) `)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),((X,I,G) `)] is set
(X,K,G) \ (X,RK1,G) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,RK1,G)) is Element of the carrier of X
[(X,K,G),(X,RK1,G)] is set
{(X,K,G),(X,RK1,G)} is non empty set
{{(X,K,G),(X,RK1,G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,RK1,G)] is set
(X,RK1,G) \ (X,RK1,G) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),(X,RK1,G)) is Element of the carrier of X
[(X,RK1,G),(X,RK1,G)] is set
{(X,RK1,G),(X,RK1,G)} is non empty set
{{(X,RK1,G),(X,RK1,G)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),(X,RK1,G)] is set
((X,RK1,G) \ (X,RK1,G)) \ ((X,I,G) `) is Element of the carrier of X
the InternalDiff of X . (((X,RK1,G) \ (X,RK1,G)),((X,I,G) `)) is Element of the carrier of X
[((X,RK1,G) \ (X,RK1,G)),((X,I,G) `)] is set
{((X,RK1,G) \ (X,RK1,G)),((X,I,G) `)} is non empty set
{((X,RK1,G) \ (X,RK1,G))} is non empty set
{{((X,RK1,G) \ (X,RK1,G)),((X,I,G) `)},{((X,RK1,G) \ (X,RK1,G))}} is non empty set
the InternalDiff of X . [((X,RK1,G) \ (X,RK1,G)),((X,I,G) `)] is set
((X,I,G) `) ` is Element of the carrier of X
(0. X) \ ((X,I,G) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,I,G) `)) is Element of the carrier of X
[(0. X),((X,I,G) `)] is set
{(0. X),((X,I,G) `)} is non empty set
{{(0. X),((X,I,G) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,I,G) `)] is set
RK - K is V92() V93() integer ext-real Element of INT
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK - RK1 is V92() V93() integer ext-real Element of INT
RK1 + (RK - RK1) is V92() V93() integer ext-real Element of INT
(X,(RK1 + (RK - RK1)),G) is Element of the carrier of X
(X,RK1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{G} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,G) is Element of the carrier of X
(X) . (G,I) is set
[G,I] is set
{G,I} is non empty set
{{G,I},{G}} is non empty set
(X) . [G,I] is set
(X,I,G) ` is Element of the carrier of X
(0. X) \ (X,I,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,I,G)) is Element of the carrier of X
[(0. X),(X,I,G)] is set
{(0. X),(X,I,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,I,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,I,G)] is set
(X,RK1,G) \ ((X,I,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),((X,I,G) `)) is Element of the carrier of X
[(X,RK1,G),((X,I,G) `)] is set
{(X,RK1,G),((X,I,G) `)} is non empty set
{(X,RK1,G)} is non empty set
{{(X,RK1,G),((X,I,G) `)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),((X,I,G) `)] is set
(X,RK1,G) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),(X,RK,G)) is Element of the carrier of X
[(X,RK1,G),(X,RK,G)] is set
{(X,RK1,G),(X,RK,G)} is non empty set
{{(X,RK1,G),(X,RK,G)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),(X,RK,G)] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,I,(G `)) is Element of the carrier of X
(X) . ((G `),I) is set
[(G `),I] is set
{(G `),I} is non empty set
{(G `)} is non empty set
{{(G `),I},{(G `)}} is non empty set
(X) . [(G `),I] is set
- I is V92() V93() integer ext-real non positive Element of INT
(X,(- I),G) is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is V92() V93() integer ext-real set
(X,K,G) is Element of the carrier of X
RK is V92() V93() integer ext-real set
(X,RK,G) is Element of the carrier of X
(X,K,G) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((X,K,G),(X,RK,G)) is Element of the carrier of X
[(X,K,G),(X,RK,G)] is set
{(X,K,G),(X,RK,G)} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),(X,RK,G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,RK,G)] is set
K - RK is V92() V93() integer ext-real Element of INT
(X,(K - RK),G) is Element of the carrier of X
K - 0 is V92() V93() integer ext-real Element of INT
(X,(K - 0),G) is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(X,K,G) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(0. X)) is Element of the carrier of X
[(X,K,G),(0. X)] is set
{(X,K,G),(0. X)} is non empty set
{{(X,K,G),(0. X)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(0. X)] is set
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,K,G) \ (X,0,G) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,0,G)) is Element of the carrier of X
[(X,K,G),(X,0,G)] is set
{(X,K,G),(X,0,G)} is non empty set
{{(X,K,G),(X,0,G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,0,G)] is set
- RK is V92() V93() integer ext-real Element of INT
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
abs RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs RK)) is Element of the carrier of X
[(G `),(abs RK)] is set
{(G `),(abs RK)} is non empty set
{(G `)} is non empty set
{{(G `),(abs RK)},{(G `)}} is non empty set
(X) . [(G `),(abs RK)] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,(G `)) is Element of the carrier of X
(X) . ((G `),I) is set
[(G `),I] is set
{(G `),I} is non empty set
{{(G `),I},{(G `)}} is non empty set
(X) . [(G `),I] is set
(X,I,G) is Element of the carrier of X
(X) . (G,I) is set
[G,I] is set
{G,I} is non empty set
{G} is non empty set
{{G,I},{G}} is non empty set
(X) . [G,I] is set
(X,I,G) ` is Element of the carrier of X
(0. X) \ (X,I,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,I,G)) is Element of the carrier of X
[(0. X),(X,I,G)] is set
{(0. X),(X,I,G)} is non empty set
{{(0. X),(X,I,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,I,G)] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK1,G) is Element of the carrier of X
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
(X,RK1,G) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((X,RK1,G),(X,RK,G)) is Element of the carrier of X
[(X,RK1,G),(X,RK,G)] is set
{(X,RK1,G),(X,RK,G)} is non empty set
{(X,RK1,G)} is non empty set
{{(X,RK1,G),(X,RK,G)},{(X,RK1,G)}} is non empty set
the InternalDiff of X . [(X,RK1,G),(X,RK,G)] is set
RK1 + I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(RK1 + I),G) is Element of the carrier of X
(X) . (G,(RK1 + I)) is set
[G,(RK1 + I)] is set
{G,(RK1 + I)} is non empty set
{{G,(RK1 + I)},{G}} is non empty set
(X) . [G,(RK1 + I)] is set
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,0,G) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((X,0,G),(X,K1,G)) is Element of the carrier of X
[(X,0,G),(X,K1,G)] is set
{(X,0,G),(X,K1,G)} is non empty set
{(X,0,G)} is non empty set
{{(X,0,G),(X,K1,G)},{(X,0,G)}} is non empty set
the InternalDiff of X . [(X,0,G),(X,K1,G)] is set
(X,K1,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,K1,(G `)) is Element of the carrier of X
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{(G `)} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
- K1 is V92() V93() integer ext-real non positive Element of INT
(X,(- K1),G) is Element of the carrier of X
- RK is V92() V93() integer ext-real Element of INT
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
abs RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs RK)) is Element of the carrier of X
[(G `),(abs RK)] is set
{(G `),(abs RK)} is non empty set
{(G `)} is non empty set
{{(G `),(abs RK)},{(G `)}} is non empty set
(X) . [(G `),(abs RK)] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK1,(G `)) is Element of the carrier of X
(X) . ((G `),RK1) is set
[(G `),RK1] is set
{(G `),RK1} is non empty set
{{(G `),RK1},{(G `)}} is non empty set
(X) . [(G `),RK1] is set
(X,RK1,G) is Element of the carrier of X
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{G} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
(X,RK1,G) ` is Element of the carrier of X
(0. X) \ (X,RK1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK1,G)) is Element of the carrier of X
[(0. X),(X,RK1,G)] is set
{(0. X),(X,RK1,G)} is non empty set
{{(0. X),(X,RK1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK1,G)] is set
(X,0,G) is Element of the carrier of X
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,0,G) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((X,0,G),(X,RK,G)) is Element of the carrier of X
[(X,0,G),(X,RK,G)] is set
{(X,0,G),(X,RK,G)} is non empty set
{(X,0,G)} is non empty set
{{(X,0,G),(X,RK,G)},{(X,0,G)}} is non empty set
the InternalDiff of X . [(X,0,G),(X,RK,G)] is set
0 + RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(0 + RK1),G) is Element of the carrier of X
(X) . (G,(0 + RK1)) is set
[G,(0 + RK1)] is set
{G,(0 + RK1)} is non empty set
{{G,(0 + RK1)},{G}} is non empty set
(X) . [G,(0 + RK1)] is set
- K is V92() V93() integer ext-real Element of INT
- (K - RK) is V92() V93() integer ext-real Element of INT
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),RI) is set
[(G `),RI] is set
{(G `),RI} is non empty set
{(G `)} is non empty set
{{(G `),RI},{(G `)}} is non empty set
(X) . [(G `),RI] is set
(X,RI,(G `)) ` is Element of the carrier of X
(0. X) \ (X,RI,(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RI,(G `))) is Element of the carrier of X
[(0. X),(X,RI,(G `))] is set
{(0. X),(X,RI,(G `))} is non empty set
{{(0. X),(X,RI,(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RI,(G `))] is set
f is Element of AtomSet X
f ` is Element of the carrier of X
(0. X) \ f is Element of the carrier of X
the InternalDiff of X . ((0. X),f) is Element of the carrier of X
[(0. X),f] is set
{(0. X),f} is non empty set
{{(0. X),f},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),f] is set
(X,RI,(f `)) is Element of the carrier of X
(X) . ((f `),RI) is set
[(f `),RI] is set
{(f `),RI} is non empty set
{(f `)} is non empty set
{{(f `),RI},{(f `)}} is non empty set
(X) . [(f `),RI] is set
(X,RI,G) is Element of the carrier of X
(X) . (G,RI) is set
[G,RI] is set
{G,RI} is non empty set
{G} is non empty set
{{G,RI},{G}} is non empty set
(X) . [G,RI] is set
abs K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs K)) is Element of the carrier of X
[(G `),(abs K)] is set
{(G `),(abs K)} is non empty set
{{(G `),(abs K)},{(G `)}} is non empty set
(X) . [(G `),(abs K)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,(G `)) is Element of the carrier of X
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
K - RI is V92() V93() integer ext-real Element of INT
(X,(K - RI),G) is Element of the carrier of X
abs (K - RI) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (K - RI))) is Element of the carrier of X
[(G `),(abs (K - RI))] is set
{(G `),(abs (K - RI))} is non empty set
{{(G `),(abs (K - RI))},{(G `)}} is non empty set
(X) . [(G `),(abs (K - RI))] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,(G `)) is Element of the carrier of X
(X) . ((G `),I) is set
[(G `),I] is set
{(G `),I} is non empty set
{{(G `),I},{(G `)}} is non empty set
(X) . [(G `),I] is set
RI + K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(RI + K1),f) is Element of the carrier of X
(X) . (f,(RI + K1)) is set
[f,(RI + K1)] is set
{f,(RI + K1)} is non empty set
{f} is non empty set
{{f,(RI + K1)},{f}} is non empty set
(X) . [f,(RI + K1)] is set
(X,K1,(G `)) \ ((X,RI,(G `)) `) is Element of the carrier of X
the InternalDiff of X . ((X,K1,(G `)),((X,RI,(G `)) `)) is Element of the carrier of X
[(X,K1,(G `)),((X,RI,(G `)) `)] is set
{(X,K1,(G `)),((X,RI,(G `)) `)} is non empty set
{(X,K1,(G `))} is non empty set
{{(X,K1,(G `)),((X,RI,(G `)) `)},{(X,K1,(G `))}} is non empty set
the InternalDiff of X . [(X,K1,(G `)),((X,RI,(G `)) `)] is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
- RK is V92() V93() integer ext-real Element of INT
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
abs RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs RK)) is Element of the carrier of X
[(G `),(abs RK)] is set
{(G `),(abs RK)} is non empty set
{(G `)} is non empty set
{{(G `),(abs RK)},{(G `)}} is non empty set
(X) . [(G `),(abs RK)] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,(G `)) is Element of the carrier of X
(X) . ((G `),I) is set
[(G `),I] is set
{(G `),I} is non empty set
{{(G `),I},{(G `)}} is non empty set
(X) . [(G `),I] is set
abs K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs K)) is Element of the carrier of X
[(G `),(abs K)] is set
{(G `),(abs K)} is non empty set
{{(G `),(abs K)},{(G `)}} is non empty set
(X) . [(G `),(abs K)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,(G `)) is Element of the carrier of X
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
K1 - I is V92() V93() integer ext-real Element of INT
RK1 is Element of AtomSet X
(X,(K1 - I),RK1) is Element of the carrier of X
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
- RI is V92() V93() integer ext-real non positive Element of INT
(X,(- RI),G) is Element of the carrier of X
I - K1 is V92() V93() integer ext-real Element of INT
RK1 ` is Element of the carrier of X
(0. X) \ RK1 is Element of the carrier of X
the InternalDiff of X . ((0. X),RK1) is Element of the carrier of X
[(0. X),RK1] is set
{(0. X),RK1} is non empty set
{{(0. X),RK1},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),RK1] is set
abs (K1 - I) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((RK1 `),(abs (K1 - I))) is Element of the carrier of X
[(RK1 `),(abs (K1 - I))] is set
{(RK1 `),(abs (K1 - I))} is non empty set
{(RK1 `)} is non empty set
{{(RK1 `),(abs (K1 - I))},{(RK1 `)}} is non empty set
(X) . [(RK1 `),(abs (K1 - I))] is set
- (K1 - I) is V92() V93() integer ext-real Element of INT
(X) . ((RK1 `),(- (K1 - I))) is set
[(RK1 `),(- (K1 - I))] is set
{(RK1 `),(- (K1 - I))} is non empty set
{{(RK1 `),(- (K1 - I))},{(RK1 `)}} is non empty set
(X) . [(RK1 `),(- (K1 - I))] is set
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,G) is Element of the carrier of X
(X) . (G,RI) is set
[G,RI] is set
{G,RI} is non empty set
{G} is non empty set
{{G,RI},{G}} is non empty set
(X) . [G,RI] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of AtomSet X
K is V92() V93() integer ext-real set
(X,K,G) is Element of the carrier of X
RK is V92() V93() integer ext-real set
(X,RK,(X,K,G)) is Element of the carrier of X
K * RK is V92() V93() integer ext-real Element of INT
(X,(K * RK),G) is Element of the carrier of X
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{G} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,RK1,(X,K1,G)) is Element of the carrier of X
(X) . ((X,K1,G),RK1) is set
[(X,K1,G),RK1] is set
{(X,K1,G),RK1} is non empty set
{(X,K1,G)} is non empty set
{{(X,K1,G),RK1},{(X,K1,G)}} is non empty set
(X) . [(X,K1,G),RK1] is set
K1 * RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K1 * RK1),G) is Element of the carrier of X
(X) . (G,(K1 * RK1)) is set
[G,(K1 * RK1)] is set
{G,(K1 * RK1)} is non empty set
{{G,(K1 * RK1)},{G}} is non empty set
(X) . [G,(K1 * RK1)] is set
- RK is V92() V93() integer ext-real Element of INT
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * RK is V92() V93() integer ext-real Element of INT
- (RK1 * RK) is V92() V93() integer ext-real Element of INT
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,RK1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,RK1) is set
[G,RK1] is set
{G,RK1} is non empty set
{G} is non empty set
{{G,RK1},{G}} is non empty set
(X) . [G,RK1] is set
(X,(RK1 * RK),G) is Element of the carrier of X
abs (RK1 * RK) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (RK1 * RK))) is Element of the carrier of X
[(G `),(abs (RK1 * RK))] is set
{(G `),(abs (RK1 * RK))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (RK1 * RK))},{(G `)}} is non empty set
(X) . [(G `),(abs (RK1 * RK))] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,(G `)) is Element of the carrier of X
(X) . ((G `),I) is set
[(G `),I] is set
{(G `),I} is non empty set
{{(G `),I},{(G `)}} is non empty set
(X) . [(G `),I] is set
RK1 * (- RK) is V92() V93() integer ext-real Element of INT
(X,(RK1 * (- RK)),(G `)) is Element of the carrier of X
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RI is Element of AtomSet X
(X,RK1,RI) is Element of the carrier of X
(X) . (RI,RK1) is set
[RI,RK1] is set
{RI,RK1} is non empty set
{RI} is non empty set
{{RI,RK1},{RI}} is non empty set
(X) . [RI,RK1] is set
(X,K1,(X,RK1,RI)) is Element of the carrier of X
(X) . ((X,RK1,RI),K1) is set
[(X,RK1,RI),K1] is set
{(X,RK1,RI),K1} is non empty set
{(X,RK1,RI)} is non empty set
{{(X,RK1,RI),K1},{(X,RK1,RI)}} is non empty set
(X) . [(X,RK1,RI),K1] is set
(X,RK1,G) ` is Element of the carrier of X
(0. X) \ (X,RK1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK1,G)) is Element of the carrier of X
[(0. X),(X,RK1,G)] is set
{(0. X),(X,RK1,G)} is non empty set
{{(0. X),(X,RK1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK1,G)] is set
(X,K1,((X,RK1,G) `)) is Element of the carrier of X
(X) . (((X,RK1,G) `),K1) is set
[((X,RK1,G) `),K1] is set
{((X,RK1,G) `),K1} is non empty set
{((X,RK1,G) `)} is non empty set
{{((X,RK1,G) `),K1},{((X,RK1,G) `)}} is non empty set
(X) . [((X,RK1,G) `),K1] is set
- K1 is V92() V93() integer ext-real non positive Element of INT
f is Element of AtomSet X
(X,(- K1),f) is Element of the carrier of X
- (- RK) is V92() V93() integer ext-real Element of INT
(X,(- (- RK)),(X,RK1,G)) is Element of the carrier of X
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * RK is V92() V93() integer ext-real Element of INT
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(X,0,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,0) is set
[G,0] is set
{G,0} is non empty set
{G} is non empty set
{{G,0},{G}} is non empty set
(X) . [G,0] is set
(X,RK,(X,0,G)) is Element of the carrier of X
(X,RK,(0. X)) is Element of the carrier of X
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
abs RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . (((0. X) `),(abs RK)) is Element of the carrier of X
[((0. X) `),(abs RK)] is set
{((0. X) `),(abs RK)} is non empty set
{((0. X) `)} is non empty set
{{((0. X) `),(abs RK)},{((0. X) `)}} is non empty set
(X) . [((0. X) `),(abs RK)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,((0. X) `)) is Element of the carrier of X
(X) . (((0. X) `),K1) is set
[((0. X) `),K1] is set
{((0. X) `),K1} is non empty set
{{((0. X) `),K1},{((0. X) `)}} is non empty set
(X) . [((0. X) `),K1] is set
I is Element of AtomSet X
(X,K1,I) is Element of the carrier of X
(X) . (I,K1) is set
[I,K1] is set
{I,K1} is non empty set
{I} is non empty set
{{I,K1},{I}} is non empty set
(X) . [I,K1] is set
(X,K1,I) ` is Element of the carrier of X
(0. X) \ (X,K1,I) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,I)) is Element of the carrier of X
[(0. X),(X,K1,I)] is set
{(0. X),(X,K1,I)} is non empty set
{{(0. X),(X,K1,I)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,I)] is set
(X,(RK1 * RK),G) is Element of the carrier of X
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * RK is V92() V93() integer ext-real Element of INT
- K is V92() V93() integer ext-real Element of INT
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K * RK1 is V92() V93() integer ext-real Element of INT
- (K * RK1) is V92() V93() integer ext-real Element of INT
0 * RK1 is empty V24() V25() V26() V28() V29() V30() V92() V93() integer ext-real non positive non negative Element of NAT
(X,(K * RK1),G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
abs (K * RK1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs (K * RK1))) is Element of the carrier of X
[(G `),(abs (K * RK1))] is set
{(G `),(abs (K * RK1))} is non empty set
{(G `)} is non empty set
{{(G `),(abs (K * RK1))},{(G `)}} is non empty set
(X) . [(G `),(abs (K * RK1))] is set
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,(G `)) is Element of the carrier of X
(X) . ((G `),RI) is set
[(G `),RI] is set
{(G `),RI} is non empty set
{{(G `),RI},{(G `)}} is non empty set
(X) . [(G `),RI] is set
(- K) * RK1 is V92() V93() integer ext-real Element of INT
(X,((- K) * RK1),(G `)) is Element of the carrier of X
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
I is Element of AtomSet X
(X,K1,I) is Element of the carrier of X
(X) . (I,K1) is set
[I,K1] is set
{I,K1} is non empty set
{I} is non empty set
{{I,K1},{I}} is non empty set
(X) . [I,K1] is set
(X,RK1,(X,K1,I)) is Element of the carrier of X
(X) . ((X,K1,I),RK1) is set
[(X,K1,I),RK1] is set
{(X,K1,I),RK1} is non empty set
{(X,K1,I)} is non empty set
{{(X,K1,I),RK1},{(X,K1,I)}} is non empty set
(X) . [(X,K1,I),RK1] is set
- K1 is V92() V93() integer ext-real non positive Element of INT
(X,(- K1),G) is Element of the carrier of X
(X,RK1,(X,(- K1),G)) is Element of the carrier of X
(X) . ((X,(- K1),G),RK1) is set
[(X,(- K1),G),RK1] is set
{(X,(- K1),G),RK1} is non empty set
{(X,(- K1),G)} is non empty set
{{(X,(- K1),G),RK1},{(X,(- K1),G)}} is non empty set
(X) . [(X,(- K1),G),RK1] is set
RK1 is Element of AtomSet X
(X,0,RK1) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (RK1,0) is set
[RK1,0] is set
{RK1,0} is non empty set
{RK1} is non empty set
{{RK1,0},{RK1}} is non empty set
(X) . [RK1,0] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
K * 0 is V92() V93() integer ext-real Element of INT
(X,(K * 0),G) is Element of the carrier of X
- RK is V92() V93() integer ext-real Element of INT
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{G} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
I is Element of AtomSet X
I ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ I is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),I) is Element of the carrier of X
[(0. X),I] is set
{(0. X),I} is non empty set
{(0. X)} is non empty set
{{(0. X),I},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),I] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
abs K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X) . ((G `),(abs K)) is Element of the carrier of X
[(G `),(abs K)] is set
{(G `),(abs K)} is non empty set
{(G `)} is non empty set
{{(G `),(abs K)},{(G `)}} is non empty set
(X) . [(G `),(abs K)] is set
(X,K1,(G `)) is Element of the carrier of X
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
- RK1 is V92() V93() integer ext-real non positive Element of INT
RI is Element of AtomSet X
(X,(- RK1),RI) is Element of the carrier of X
RI ` is Element of the carrier of X
(0. X) \ RI is Element of the carrier of X
the InternalDiff of X . ((0. X),RI) is Element of the carrier of X
[(0. X),RI] is set
{(0. X),RI} is non empty set
{{(0. X),RI},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),RI] is set
(X,RK1,(RI `)) is Element of the carrier of X
(X) . ((RI `),RK1) is set
[(RI `),RK1] is set
{(RI `),RK1} is non empty set
{(RI `)} is non empty set
{{(RI `),RK1},{(RI `)}} is non empty set
(X) . [(RI `),RK1] is set
(X,RK1,I) is Element of the carrier of X
(X) . (I,RK1) is set
[I,RK1] is set
{I,RK1} is non empty set
{I} is non empty set
{{I,RK1},{I}} is non empty set
(X) . [I,RK1] is set
(- K) * (- RK) is V92() V93() integer ext-real Element of INT
(X,((- K) * (- RK)),G) is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G is Element of AtomSet X
K is V92() V93() integer ext-real set
(X,K,G) is Element of the carrier of X
RK is V92() V93() integer ext-real set
K + RK is V92() V93() integer ext-real Element of INT
(X,(K + RK),G) is Element of the carrier of X
(X,RK,G) is Element of the carrier of X
(X,RK,G) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
(X,K,G) \ ((X,RK,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,RK,G) `)) is Element of the carrier of X
[(X,K,G),((X,RK,G) `)] is set
{(X,K,G),((X,RK,G) `)} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),((X,RK,G) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,RK,G) `)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{G} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,K1,G) ` is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
(X,K,G) \ ((X,K1,G) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,K1,G) `)) is Element of the carrier of X
[(X,K,G),((X,K1,G) `)] is set
{(X,K,G),((X,K1,G) `)} is non empty set
{{(X,K,G),((X,K1,G) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,K1,G) `)] is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,K1,(G `)) is Element of the carrier of X
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{(G `)} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
(X,K,G) \ (X,K1,(G `)) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,K1,(G `))) is Element of the carrier of X
[(X,K,G),(X,K1,(G `))] is set
{(X,K,G),(X,K1,(G `))} is non empty set
{{(X,K,G),(X,K1,(G `))},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,K1,(G `))] is set
- K1 is V92() V93() integer ext-real non positive Element of INT
(X,(- K1),G) is Element of the carrier of X
(X,K,G) \ (X,(- K1),G) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,(- K1),G)) is Element of the carrier of X
[(X,K,G),(X,(- K1),G)] is set
{(X,K,G),(X,(- K1),G)} is non empty set
{{(X,K,G),(X,(- K1),G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,(- K1),G)] is set
K - (- K1) is V92() V93() integer ext-real Element of INT
(X,(K - (- K1)),G) is Element of the carrier of X
(X,K,G) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(0. X)) is Element of the carrier of X
[(X,K,G),(0. X)] is set
{(X,K,G),(0. X)} is non empty set
{{(X,K,G),(0. X)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(0. X)] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
(X,K,G) \ ((0. X) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((0. X) `)) is Element of the carrier of X
[(X,K,G),((0. X) `)] is set
{(X,K,G),((0. X) `)} is non empty set
{{(X,K,G),((0. X) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((0. X) `)] is set
- RK is V92() V93() integer ext-real Element of INT
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
- (- RK) is V92() V93() integer ext-real Element of INT
(X,(- (- RK)),G) is Element of the carrier of X
(X,(- (- RK)),G) ` is Element of the carrier of X
(0. X) \ (X,(- (- RK)),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(- (- RK)),G)) is Element of the carrier of X
[(0. X),(X,(- (- RK)),G)] is set
{(0. X),(X,(- (- RK)),G)} is non empty set
{{(0. X),(X,(- (- RK)),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(- (- RK)),G)] is set
(X,K,G) \ ((X,(- (- RK)),G) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,(- (- RK)),G) `)) is Element of the carrier of X
[(X,K,G),((X,(- (- RK)),G) `)] is set
{(X,K,G),((X,(- (- RK)),G) `)} is non empty set
{{(X,K,G),((X,(- (- RK)),G) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,(- (- RK)),G) `)] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),K1) is set
[(G `),K1] is set
{(G `),K1} is non empty set
{(G `)} is non empty set
{{(G `),K1},{(G `)}} is non empty set
(X) . [(G `),K1] is set
(X,K1,(G `)) ` is Element of the carrier of X
(0. X) \ (X,K1,(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,(G `))) is Element of the carrier of X
[(0. X),(X,K1,(G `))] is set
{(0. X),(X,K1,(G `))} is non empty set
{{(0. X),(X,K1,(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,(G `))] is set
(X,K,G) \ ((X,K1,(G `)) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),((X,K1,(G `)) `)) is Element of the carrier of X
[(X,K,G),((X,K1,(G `)) `)] is set
{(X,K,G),((X,K1,(G `)) `)} is non empty set
{{(X,K,G),((X,K1,(G `)) `)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),((X,K1,(G `)) `)] is set
RK1 is Element of AtomSet X
RK1 ` is Element of the carrier of X
(0. X) \ RK1 is Element of the carrier of X
the InternalDiff of X . ((0. X),RK1) is Element of the carrier of X
[(0. X),RK1] is set
{(0. X),RK1} is non empty set
{{(0. X),RK1},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),RK1] is set
(X,K1,(RK1 `)) is Element of the carrier of X
(X) . ((RK1 `),K1) is set
[(RK1 `),K1] is set
{(RK1 `),K1} is non empty set
{(RK1 `)} is non empty set
{{(RK1 `),K1},{(RK1 `)}} is non empty set
(X) . [(RK1 `),K1] is set
(X,K,G) \ (X,K1,(RK1 `)) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,K1,(RK1 `))) is Element of the carrier of X
[(X,K,G),(X,K1,(RK1 `))] is set
{(X,K,G),(X,K1,(RK1 `))} is non empty set
{{(X,K,G),(X,K1,(RK1 `))},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,K1,(RK1 `))] is set
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{G} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,K,G) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((X,K,G),(X,K1,G)) is Element of the carrier of X
[(X,K,G),(X,K1,G)] is set
{(X,K,G),(X,K1,G)} is non empty set
{{(X,K,G),(X,K1,G)},{(X,K,G)}} is non empty set
the InternalDiff of X . [(X,K,G),(X,K1,G)] is set
K - K1 is V92() V93() integer ext-real Element of INT
(X,(K - K1),G) is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
BCK-part X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{G} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
K1 is Element of the carrier of X
K is Element of AtomSet X
(X,RK,K) is Element of the carrier of X
(X) . (K,RK) is set
[K,RK] is set
{K,RK} is non empty set
{K} is non empty set
{{K,RK},{K}} is non empty set
(X) . [K,RK] is set
(X,RK,K) ` is Element of the carrier of X
(0. X) \ (X,RK,K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,K)) is Element of the carrier of X
[(0. X),(X,RK,K)] is set
{(0. X),(X,RK,K)} is non empty set
{{(0. X),(X,RK,K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,K)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK,G) is Element of the carrier of X
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
G is Element of AtomSet X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
BCK-part X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{(0. X)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
RK is Element of the carrier of X
RK is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
0 + 1 is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,1) is set
[G,1] is set
{G,1} is non empty set
{G} is non empty set
{{G,1},{G}} is non empty set
(X) . [G,1] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
G is Element of the carrier of X
K is Element of the carrier of X
G \ K is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (G,K) is Element of the carrier of X
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
the InternalDiff of X . [G,K] is set
(G \ K) \ G is Element of the carrier of X
the InternalDiff of X . ((G \ K),G) is Element of the carrier of X
[(G \ K),G] is set
{(G \ K),G} is non empty set
{(G \ K)} is non empty set
{{(G \ K),G},{(G \ K)}} is non empty set
the InternalDiff of X . [(G \ K),G] is set
(X,K) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,1,K) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (K,1) is set
[K,1] is set
{K,1} is non empty set
{K} is non empty set
{{K,1},{K}} is non empty set
(X) . [K,1] is set
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
G \ G is Element of the carrier of X
the InternalDiff of X . (G,G) is Element of the carrier of X
[G,G] is set
{G,G} is non empty set
{{G,G},{G}} is non empty set
the InternalDiff of X . [G,G] is set
(G \ G) \ K is Element of the carrier of X
the InternalDiff of X . ((G \ G),K) is Element of the carrier of X
[(G \ G),K] is set
{(G \ G),K} is non empty set
{(G \ G)} is non empty set
{{(G \ G),K},{(G \ G)}} is non empty set
the InternalDiff of X . [(G \ G),K] is set
K ` is Element of the carrier of X
(0. X) \ K is Element of the carrier of X
the InternalDiff of X . ((0. X),K) is Element of the carrier of X
[(0. X),K] is set
{(0. X),K} is non empty set
{(0. X)} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K] is set
RK is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of the carrier of X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K is Element of AtomSet X
BranchV K is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K <= b₁ } is set
(X,K) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,1,K) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (K,1) is set
[K,1] is set
{K,1} is non empty set
{K} is non empty set
{{K,1},{K}} is non empty set
(X) . [K,1] is set
BCK-part X is non empty Element of bool the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
K ` is Element of the carrier of X
(0. X) \ K is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),K) is Element of the carrier of X
[(0. X),K] is set
{(0. X),K} is non empty set
{(0. X)} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K] is set
K1 is Element of the carrier of X
K1 is Element of the carrier of X
(X,1,G) is Element of the carrier of X
(X) . (G,1) is set
[G,1] is set
{G,1} is non empty set
{G} is non empty set
{{G,1},{G}} is non empty set
(X) . [G,1] is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
K ` is Element of the carrier of X
(0. X) \ K is Element of the carrier of X
the InternalDiff of X . ((0. X),K) is Element of the carrier of X
[(0. X),K] is set
{(0. X),K} is non empty set
{{(0. X),K},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),K] is set
BCK-part X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K1) is set
[G,K1] is set
{G,K1} is non empty set
{G} is non empty set
{{G,K1},{G}} is non empty set
(X) . [G,K1] is set
(X,K1,G) ` is Element of the carrier of X
(0. X) \ (X,K1,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,G)) is Element of the carrier of X
[(0. X),(X,K1,G)] is set
{(0. X),(X,K1,G)} is non empty set
{{(0. X),(X,K1,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,G)] is set
RK1 is Element of the carrier of X
(X,K1,(K `)) is Element of the carrier of X
(X) . ((K `),K1) is set
[(K `),K1] is set
{(K `),K1} is non empty set
{(K `)} is non empty set
{{(K `),K1},{(K `)}} is non empty set
(X) . [(K `),K1] is set
(X,K1,K) is Element of the carrier of X
(X) . (K,K1) is set
[K,K1] is set
{K,K1} is non empty set
{K} is non empty set
{{K,K1},{K}} is non empty set
(X) . [K,K1] is set
(X,K1,K) ` is Element of the carrier of X
(0. X) \ (X,K1,K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K1,K)) is Element of the carrier of X
[(0. X),(X,K1,K)] is set
{(0. X),(X,K1,K)} is non empty set
{{(0. X),(X,K1,K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K1,K)] is set
(X,(X,K),K) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (K,(X,K)) is set
[K,(X,K)] is set
{K,(X,K)} is non empty set
{K} is non empty set
{{K,(X,K)},{K}} is non empty set
(X) . [K,(X,K)] is set
(X,(X,K),K) ` is Element of the carrier of X
(0. X) \ (X,(X,K),K) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,K),K)) is Element of the carrier of X
[(0. X),(X,(X,K),K)] is set
{(0. X),(X,(X,K),K)} is non empty set
{{(0. X),(X,(X,K),K)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,K),K)] is set
K1 is Element of the carrier of X
(X,(X,K),(G `)) is Element of the carrier of X
(X) . ((G `),(X,K)) is set
[(G `),(X,K)] is set
{(G `),(X,K)} is non empty set
{(G `)} is non empty set
{{(G `),(X,K)},{(G `)}} is non empty set
(X) . [(G `),(X,K)] is set
(X,(X,K),G) is Element of the carrier of X
(X) . (G,(X,K)) is set
[G,(X,K)] is set
{G,(X,K)} is non empty set
{G} is non empty set
{{G,(X,K)},{G}} is non empty set
(X) . [G,(X,K)] is set
(X,(X,K),G) ` is Element of the carrier of X
(0. X) \ (X,(X,K),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,K),G)) is Element of the carrier of X
[(0. X),(X,(X,K),G)] is set
{(0. X),(X,(X,K),G)} is non empty set
{{(0. X),(X,(X,K),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,K),G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
G is Element of the carrier of X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,RK,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,RK) is set
[G,RK] is set
{G,RK} is non empty set
{G} is non empty set
{{G,RK},{G}} is non empty set
(X) . [G,RK] is set
AtomSet X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G ` is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
K1 is Element of AtomSet X
(X,K,K1) is Element of the carrier of X
(X) . (K1,K) is set
[K1,K] is set
{K1,K} is non empty set
{K1} is non empty set
{{K1,K},{K1}} is non empty set
(X) . [K1,K] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,I,G) is Element of the carrier of X
(X) . (G,I) is set
[G,I] is set
{G,I} is non empty set
{{G,I},{G}} is non empty set
(X) . [G,I] is set
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,G) is Element of the carrier of X
(X) . (G,RI) is set
[G,RI] is set
{G,RI} is non empty set
{{G,RI},{G}} is non empty set
(X) . [G,RI] is set
f is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K + f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f is Element of AtomSet X
f \ G is Element of the carrier of X
the InternalDiff of X . (f,G) is Element of the carrier of X
[f,G] is set
{f,G} is non empty set
{f} is non empty set
{{f,G},{f}} is non empty set
the InternalDiff of X . [f,G] is set
BranchV f is non empty Element of bool the carrier of X
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : f <= b<sub>1</sub> } is set
(X,f) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K,f) is Element of the carrier of X
(X) . (f,K) is set
[f,K] is set
{f,K} is non empty set
{{f,K},{f}} is non empty set
(X) . [f,K] is set
(X,K,f) ` is Element of the carrier of X
(0. X) \ (X,K,f) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,f)) is Element of the carrier of X
[(0. X),(X,K,f)] is set
{(0. X),(X,K,f)} is non empty set
{{(0. X),(X,K,f)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,f)] is set
y is Element of the carrier of X
(X,I,G) ` is Element of the carrier of X
(0. X) \ (X,I,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,I,G)) is Element of the carrier of X
[(0. X),(X,I,G)] is set
{(0. X),(X,I,G)} is non empty set
{{(0. X),(X,I,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,I,G)] is set
y is Element of the carrier of X
(X,(K + f),f) is Element of the carrier of X
(X) . (f,(K + f)) is set
[f,(K + f)] is set
{f,(K + f)} is non empty set
{{f,(K + f)},{f}} is non empty set
(X) . [f,(K + f)] is set
(X,(K + f),f) ` is Element of the carrier of X
(0. X) \ (X,(K + f),f) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(K + f),f)) is Element of the carrier of X
[(0. X),(X,(K + f),f)] is set
{(0. X),(X,(K + f),f)} is non empty set
{{(0. X),(X,(K + f),f)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K + f),f)] is set
(X,f,f) is Element of the carrier of X
(X) . (f,f) is set
[f,f] is set
{f,f} is non empty set
{{f,f},{f}} is non empty set
(X) . [f,f] is set
(X,f,f) ` is Element of the carrier of X
(0. X) \ (X,f,f) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,f,f)) is Element of the carrier of X
[(0. X),(X,f,f)] is set
{(0. X),(X,f,f)} is non empty set
{{(0. X),(X,f,f)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,f,f)] is set
(X,K,f) \ ((X,f,f) `) is Element of the carrier of X
the InternalDiff of X . ((X,K,f),((X,f,f) `)) is Element of the carrier of X
[(X,K,f),((X,f,f) `)] is set
{(X,K,f),((X,f,f) `)} is non empty set
{(X,K,f)} is non empty set
{{(X,K,f),((X,f,f) `)},{(X,K,f)}} is non empty set
the InternalDiff of X . [(X,K,f),((X,f,f) `)] is set
((X,K,f) \ ((X,f,f) `)) ` is Element of the carrier of X
(0. X) \ ((X,K,f) \ ((X,f,f) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,K,f) \ ((X,f,f) `))) is Element of the carrier of X
[(0. X),((X,K,f) \ ((X,f,f) `))] is set
{(0. X),((X,K,f) \ ((X,f,f) `))} is non empty set
{{(0. X),((X,K,f) \ ((X,f,f) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,K,f) \ ((X,f,f) `))] is set
((X,f,f) `) ` is Element of the carrier of X
(0. X) \ ((X,f,f) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((X,f,f) `)) is Element of the carrier of X
[(0. X),((X,f,f) `)] is set
{(0. X),((X,f,f) `)} is non empty set
{{(0. X),((X,f,f) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((X,f,f) `)] is set
(((X,f,f) `) `) ` is Element of the carrier of X
(0. X) \ (((X,f,f) `) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(((X,f,f) `) `)) is Element of the carrier of X
[(0. X),(((X,f,f) `) `)] is set
{(0. X),(((X,f,f) `) `)} is non empty set
{{(0. X),(((X,f,f) `) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(((X,f,f) `) `)] is set
(X,f,G) is Element of the carrier of X
(X) . (G,f) is set
[G,f] is set
{G,f} is non empty set
{{G,f},{G}} is non empty set
(X) . [G,f] is set
(X,f,G) ` is Element of the carrier of X
(0. X) \ (X,f,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,f,G)) is Element of the carrier of X
[(0. X),(X,f,G)] is set
{(0. X),(X,f,G)} is non empty set
{{(0. X),(X,f,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,f,G)] is set
y is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
1 + y is non empty V24() V25() V26() V30() V92() V93() integer ext-real positive non negative Element of NAT
K * (1 + y) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K * I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K1 \ G is Element of the carrier of X
the InternalDiff of X . (K1,G) is Element of the carrier of X
[K1,G] is set
{K1,G} is non empty set
{{K1,G},{K1}} is non empty set
the InternalDiff of X . [K1,G] is set
BranchV K1 is non empty Element of bool the carrier of X
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : K1 <= b<sub>1</sub> } is set
(X,K1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K,K1) ` is Element of the carrier of X
(0. X) \ (X,K,K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,K1)) is Element of the carrier of X
[(0. X),(X,K,K1)] is set
{(0. X),(X,K,K1)} is non empty set
{{(0. X),(X,K,K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,K1)] is set
RI is Element of the carrier of X
(X,RK,K1) is Element of the carrier of X
(X) . (K1,RK) is set
[K1,RK] is set
{K1,RK} is non empty set
{{K1,RK},{K1}} is non empty set
(X) . [K1,RK] is set
(X,RK,K1) ` is Element of the carrier of X
(0. X) \ (X,RK,K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,K1)) is Element of the carrier of X
[(0. X),(X,RK,K1)] is set
{(0. X),(X,RK,K1)} is non empty set
{{(0. X),(X,RK,K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,K1)] is set
RK1 is Element of AtomSet X
(X,I,RK1) is Element of the carrier of X
(X) . (RK1,I) is set
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
(X) . [RK1,I] is set
(X,I,RK1) ` is Element of the carrier of X
(0. X) \ (X,I,RK1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,I,RK1)) is Element of the carrier of X
[(0. X),(X,I,RK1)] is set
{(0. X),(X,I,RK1)} is non empty set
{{(0. X),(X,I,RK1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,I,RK1)] is set
(X,I,(0. X)) is Element of the carrier of X
(X) . ((0. X),I) is set
[(0. X),I] is set
{(0. X),I} is non empty set
{{(0. X),I},{(0. X)}} is non empty set
(X) . [(0. X),I] is set
(X,RK,G) ` is Element of the carrier of X
(0. X) \ (X,RK,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,G)) is Element of the carrier of X
[(0. X),(X,RK,G)] is set
{(0. X),(X,RK,G)} is non empty set
{{(0. X),(X,RK,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K,G) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . (G,K) is set
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
(X) . [G,K] is set
(X,(X,K,G)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
K gcd RK is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK div (K gcd RK) is V92() V93() integer ext-real set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : b<sub>1</sub> is atom } is set
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
K1 is Element of AtomSet X
K1 \ G is Element of the carrier of X
the InternalDiff of X . (K1,G) is Element of the carrier of X
[K1,G] is set
{K1,G} is non empty set
{K1} is non empty set
{{K1,G},{K1}} is non empty set
the InternalDiff of X . [K1,G] is set
BranchV K1 is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K1 <= b₁ } is set
(X,K1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK,K1) is Element of the carrier of X
(X) . (K1,RK) is set
[K1,RK] is set
{K1,RK} is non empty set
{{K1,RK},{K1}} is non empty set
(X) . [K1,RK] is set
BCK-part X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
RK1 * I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
RK1 * f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(RK1 * RI) + 0 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f gcd RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
y is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(f gcd RI) * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(K gcd RK) * (f gcd RI) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
((K gcd RK) * (f gcd RI)) * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
x is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(f gcd RI) * x is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
((K gcd RK) * (f gcd RI)) * x is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
a is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
((K gcd RK) * (f gcd RI)) * a is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(K gcd RK) * 1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(f gcd RI) * a is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(K gcd RK) * ((f gcd RI) * a) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,y,(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),y) is set
[(X,K,G),y] is set
{(X,K,G),y} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),y},{(X,K,G)}} is non empty set
(X) . [(X,K,G),y] is set
(X,y,(X,K,G)) ` is Element of the carrier of X
(0. X) \ (X,y,(X,K,G)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,y,(X,K,G))) is Element of the carrier of X
[(0. X),(X,y,(X,K,G))] is set
{(0. X),(X,y,(X,K,G))} is non empty set
{{(0. X),(X,y,(X,K,G))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,y,(X,K,G))] is set
x is Element of the carrier of X
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
(X,y,((X,K,G) `)) is Element of the carrier of X
(X) . (((X,K,G) `),y) is set
[((X,K,G) `),y] is set
{((X,K,G) `),y} is non empty set
{((X,K,G) `)} is non empty set
{{((X,K,G) `),y},{((X,K,G) `)}} is non empty set
(X) . [((X,K,G) `),y] is set
(X,K,K1) is Element of the carrier of X
(X) . (K1,K) is set
[K1,K] is set
{K1,K} is non empty set
{{K1,K},{K1}} is non empty set
(X) . [K1,K] is set
(X,K,K1) ` is Element of the carrier of X
(0. X) \ (X,K,K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,K1)) is Element of the carrier of X
[(0. X),(X,K,K1)] is set
{(0. X),(X,K,K1)} is non empty set
{{(0. X),(X,K,K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,K1)] is set
(X,y,((X,K,K1) `)) is Element of the carrier of X
(X) . (((X,K,K1) `),y) is set
[((X,K,K1) `),y] is set
{((X,K,K1) `),y} is non empty set
{((X,K,K1) `)} is non empty set
{{((X,K,K1) `),y},{((X,K,K1) `)}} is non empty set
(X) . [((X,K,K1) `),y] is set
(X,y,(X,K,K1)) is Element of the carrier of X
(X) . ((X,K,K1),y) is set
[(X,K,K1),y] is set
{(X,K,K1),y} is non empty set
{(X,K,K1)} is non empty set
{{(X,K,K1),y},{(X,K,K1)}} is non empty set
(X) . [(X,K,K1),y] is set
(X,y,(X,K,K1)) ` is Element of the carrier of X
(0. X) \ (X,y,(X,K,K1)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,y,(X,K,K1))) is Element of the carrier of X
[(0. X),(X,y,(X,K,K1))] is set
{(0. X),(X,y,(X,K,K1))} is non empty set
{{(0. X),(X,y,(X,K,K1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,y,(X,K,K1))] is set
K * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(K * y),K1) is Element of the carrier of X
(X) . (K1,(K * y)) is set
[K1,(K * y)] is set
{K1,(K * y)} is non empty set
{{K1,(K * y)},{K1}} is non empty set
(X) . [K1,(K * y)] is set
(X,(K * y),K1) ` is Element of the carrier of X
(0. X) \ (X,(K * y),K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(K * y),K1)) is Element of the carrier of X
[(0. X),(X,(K * y),K1)] is set
{(0. X),(X,(K * y),K1)} is non empty set
{{(0. X),(X,(K * y),K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(K * y),K1)] is set
RK1 * f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(RK1 * f) * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
x is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(RK1 * RI) * x is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f * y is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * (f * y) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RI * x is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 * (RI * x) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
a is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
RI * a is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,(X,K,G)) is Element of the carrier of X
(X) . ((X,K,G),RI) is set
[(X,K,G),RI] is set
{(X,K,G),RI} is non empty set
{(X,K,G)} is non empty set
{{(X,K,G),RI},{(X,K,G)}} is non empty set
(X) . [(X,K,G),RI] is set
(X,RI,(X,K,G)) ` is Element of the carrier of X
(0. X) \ (X,RI,(X,K,G)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RI,(X,K,G))) is Element of the carrier of X
[(0. X),(X,RI,(X,K,G))] is set
{(0. X),(X,RI,(X,K,G))} is non empty set
{{(0. X),(X,RI,(X,K,G))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RI,(X,K,G))] is set
(X,K,G) ` is Element of the carrier of X
(0. X) \ (X,K,G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,G)) is Element of the carrier of X
[(0. X),(X,K,G)] is set
{(0. X),(X,K,G)} is non empty set
{{(0. X),(X,K,G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,G)] is set
(X,RI,((X,K,G) `)) is Element of the carrier of X
(X) . (((X,K,G) `),RI) is set
[((X,K,G) `),RI] is set
{((X,K,G) `),RI} is non empty set
{((X,K,G) `)} is non empty set
{{((X,K,G) `),RI},{((X,K,G) `)}} is non empty set
(X) . [((X,K,G) `),RI] is set
(X,K,K1) is Element of the carrier of X
(X) . (K1,K) is set
[K1,K] is set
{K1,K} is non empty set
{{K1,K},{K1}} is non empty set
(X) . [K1,K] is set
(X,K,K1) ` is Element of the carrier of X
(0. X) \ (X,K,K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,K,K1)) is Element of the carrier of X
[(0. X),(X,K,K1)] is set
{(0. X),(X,K,K1)} is non empty set
{{(0. X),(X,K,K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,K,K1)] is set
(X,RI,((X,K,K1) `)) is Element of the carrier of X
(X) . (((X,K,K1) `),RI) is set
[((X,K,K1) `),RI] is set
{((X,K,K1) `),RI} is non empty set
{((X,K,K1) `)} is non empty set
{{((X,K,K1) `),RI},{((X,K,K1) `)}} is non empty set
(X) . [((X,K,K1) `),RI] is set
(X,RI,(X,K,K1)) is Element of the carrier of X
(X) . ((X,K,K1),RI) is set
[(X,K,K1),RI] is set
{(X,K,K1),RI} is non empty set
{(X,K,K1)} is non empty set
{{(X,K,K1),RI},{(X,K,K1)}} is non empty set
(X) . [(X,K,K1),RI] is set
(X,RI,(X,K,K1)) ` is Element of the carrier of X
(0. X) \ (X,RI,(X,K,K1)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RI,(X,K,K1))) is Element of the carrier of X
[(0. X),(X,RI,(X,K,K1))] is set
{(0. X),(X,RI,(X,K,K1))} is non empty set
{{(0. X),(X,RI,(X,K,K1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RI,(X,K,K1))] is set
RK1 * f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(RK1 * f) * RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,((RK1 * f) * RI),K1) is Element of the carrier of X
(X) . (K1,((RK1 * f) * RI)) is set
[K1,((RK1 * f) * RI)] is set
{K1,((RK1 * f) * RI)} is non empty set
{{K1,((RK1 * f) * RI)},{K1}} is non empty set
(X) . [K1,((RK1 * f) * RI)] is set
(X,((RK1 * f) * RI),K1) ` is Element of the carrier of X
(0. X) \ (X,((RK1 * f) * RI),K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,((RK1 * f) * RI),K1)) is Element of the carrier of X
[(0. X),(X,((RK1 * f) * RI),K1)] is set
{(0. X),(X,((RK1 * f) * RI),K1)} is non empty set
{{(0. X),(X,((RK1 * f) * RI),K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,((RK1 * f) * RI),K1)] is set
RK * f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(RK * f),K1) is Element of the carrier of X
(X) . (K1,(RK * f)) is set
[K1,(RK * f)] is set
{K1,(RK * f)} is non empty set
{{K1,(RK * f)},{K1}} is non empty set
(X) . [K1,(RK * f)] is set
(X,(RK * f),K1) ` is Element of the carrier of X
(0. X) \ (X,(RK * f),K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(RK * f),K1)) is Element of the carrier of X
[(0. X),(X,(RK * f),K1)] is set
{(0. X),(X,(RK * f),K1)} is non empty set
{{(0. X),(X,(RK * f),K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(RK * f),K1)] is set
(X,f,(X,RK,K1)) is Element of the carrier of X
(X) . ((X,RK,K1),f) is set
[(X,RK,K1),f] is set
{(X,RK,K1),f} is non empty set
{(X,RK,K1)} is non empty set
{{(X,RK,K1),f},{(X,RK,K1)}} is non empty set
(X) . [(X,RK,K1),f] is set
(X,f,(X,RK,K1)) ` is Element of the carrier of X
(0. X) \ (X,f,(X,RK,K1)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,f,(X,RK,K1))) is Element of the carrier of X
[(0. X),(X,f,(X,RK,K1))] is set
{(0. X),(X,f,(X,RK,K1))} is non empty set
{{(0. X),(X,f,(X,RK,K1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,f,(X,RK,K1))] is set
(X,RK,K1) ` is Element of the carrier of X
(0. X) \ (X,RK,K1) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK,K1)) is Element of the carrier of X
[(0. X),(X,RK,K1)] is set
{(0. X),(X,RK,K1)} is non empty set
{{(0. X),(X,RK,K1)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK,K1)] is set
(X,f,((X,RK,K1) `)) is Element of the carrier of X
(X) . (((X,RK,K1) `),f) is set
[((X,RK,K1) `),f] is set
{((X,RK,K1) `),f} is non empty set
{((X,RK,K1) `)} is non empty set
{{((X,RK,K1) `),f},{((X,RK,K1) `)}} is non empty set
(X) . [((X,RK,K1) `),f] is set
(X,f,(0. X)) is Element of the carrier of X
(X) . ((0. X),f) is set
[(0. X),f] is set
{(0. X),f} is non empty set
{{(0. X),f},{(0. X)}} is non empty set
(X) . [(0. X),f] is set
y is Element of the carrier of X
RK gcd K is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK div RK1 is V92() V93() integer ext-real set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is Element of the carrier of X
G ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ G is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),G) is Element of the carrier of X
[(0. X),G] is set
{(0. X),G} is non empty set
{(0. X)} is non empty set
{{(0. X),G},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),G] is set
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(G `)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(X,(G `)),(G `)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G `),(X,(G `))) is set
[(G `),(X,(G `))] is set
{(G `),(X,(G `))} is non empty set
{(G `)} is non empty set
{{(G `),(X,(G `))},{(G `)}} is non empty set
(X) . [(G `),(X,(G `))] is set
BCK-part X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of X : 0. X <= b<sub>1</sub> } is set
(X,(X,(G `)),(G `)) ` is Element of the carrier of X
(0. X) \ (X,(X,(G `)),(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,(G `)),(G `))) is Element of the carrier of X
[(0. X),(X,(X,(G `)),(G `))] is set
{(0. X),(X,(X,(G `)),(G `))} is non empty set
{{(0. X),(X,(X,(G `)),(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,(G `)),(G `))] is set
RK is Element of the carrier of X
(G `) ` is Element of the carrier of X
(0. X) \ (G `) is Element of the carrier of X
the InternalDiff of X . ((0. X),(G `)) is Element of the carrier of X
[(0. X),(G `)] is set
{(0. X),(G `)} is non empty set
{{(0. X),(G `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(G `)] is set
(X,(X,(G `)),((G `) `)) is Element of the carrier of X
(X) . (((G `) `),(X,(G `))) is set
[((G `) `),(X,(G `))] is set
{((G `) `),(X,(G `))} is non empty set
{((G `) `)} is non empty set
{{((G `) `),(X,(G `))},{((G `) `)}} is non empty set
(X) . [((G `) `),(X,(G `))] is set
(X,(X,(G `)),((G `) `)) ` is Element of the carrier of X
(0. X) \ (X,(X,(G `)),((G `) `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,(G `)),((G `) `))) is Element of the carrier of X
[(0. X),(X,(X,(G `)),((G `) `))] is set
{(0. X),(X,(X,(G `)),((G `) `))} is non empty set
{{(0. X),(X,(X,(G `)),((G `) `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,(G `)),((G `) `))] is set
(X,(X,(G `)),G) is Element of the carrier of X
(X) . (G,(X,(G `))) is set
[G,(X,(G `))] is set
{G,(X,(G `))} is non empty set
{G} is non empty set
{{G,(X,(G `))},{G}} is non empty set
(X) . [G,(X,(G `))] is set
(X,(X,(G `)),G) ` is Element of the carrier of X
(0. X) \ (X,(X,(G `)),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,(G `)),G)) is Element of the carrier of X
[(0. X),(X,(X,(G `)),G)] is set
{(0. X),(X,(X,(G `)),G)} is non empty set
{{(0. X),(X,(X,(G `)),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,(G `)),G)] is set
(X,(X,G),G) is Element of the carrier of X
(X) . (G,(X,G)) is set
[G,(X,G)] is set
{G,(X,G)} is non empty set
{{G,(X,G)},{G}} is non empty set
(X) . [G,(X,G)] is set
(X,(X,G),G) ` is Element of the carrier of X
(0. X) \ (X,(X,G),G) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,G),G)) is Element of the carrier of X
[(0. X),(X,(X,G),G)] is set
{(0. X),(X,(X,G),G)} is non empty set
{{(0. X),(X,(X,G),G)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,G),G)] is set
K1 is Element of the carrier of X
(X,(X,G),(G `)) is Element of the carrier of X
(X) . ((G `),(X,G)) is set
[(G `),(X,G)] is set
{(G `),(X,G)} is non empty set
{{(G `),(X,G)},{(G `)}} is non empty set
(X) . [(G `),(X,G)] is set
(X,(X,G),(G `)) ` is Element of the carrier of X
(0. X) \ (X,(X,G),(G `)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,(X,G),(G `))) is Element of the carrier of X
[(0. X),(X,(X,G),(G `))] is set
{(0. X),(X,(X,G),(G `))} is non empty set
{{(0. X),(X,(X,G),(G `))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,(X,G),(G `))] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of the carrier of X
K is Element of the carrier of X
G \ K is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (G,K) is Element of the carrier of X
[G,K] is set
{G,K} is non empty set
{G} is non empty set
{{G,K},{G}} is non empty set
the InternalDiff of X . [G,K] is set
(X,(G \ K)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK is Element of AtomSet X
BranchV RK is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : RK <= b₁ } is set
BCK-part X is non empty Element of bool the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
K1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,K1,(G \ K)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G \ K),K1) is set
[(G \ K),K1] is set
{(G \ K),K1} is non empty set
{(G \ K)} is non empty set
{{(G \ K),K1},{(G \ K)}} is non empty set
(X) . [(G \ K),K1] is set
(X,1,(G \ K)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((G \ K),1) is set
[(G \ K),1] is set
{(G \ K),1} is non empty set
{(G \ K)} is non empty set
{{(G \ K),1},{(G \ K)}} is non empty set
(X) . [(G \ K),1] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is Element of the carrier of X
(X,G) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
K is Element of the carrier of X
(X,K) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,G) lcm (X,K) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK is Element of AtomSet X
BranchV RK is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : RK <= b₁ } is set
K1 is Element of AtomSet X
RK \ K1 is Element of AtomSet X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (RK,K1) is Element of the carrier of X
[RK,K1] is set
{RK,K1} is non empty set
{RK} is non empty set
{{RK,K1},{RK}} is non empty set
the InternalDiff of X . [RK,K1] is set
BranchV K1 is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : K1 <= b₁ } is set
(X,(RK \ K1)) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,K) * RK1 is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RK) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
f is V24() V25() V26() V30() V92() V93() integer ext-real non negative set
(X,G) * f is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
RI is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,RI,(RK \ K1)) is Element of the carrier of X
(X) is Relation-like [: the carrier of X,NAT:] -defined the carrier of X -valued Function-like V14([: the carrier of X,NAT:]) quasi_total Element of bool [:[: the carrier of X,NAT:], the carrier of X:]
[: the carrier of X,NAT:] is set
[:[: the carrier of X,NAT:], the carrier of X:] is set
bool [:[: the carrier of X,NAT:], the carrier of X:] is set
(X) . ((RK \ K1),RI) is set
[(RK \ K1),RI] is set
{(RK \ K1),RI} is non empty set
{(RK \ K1)} is non empty set
{{(RK \ K1),RI},{(RK \ K1)}} is non empty set
(X) . [(RK \ K1),RI] is set
(X,((X,G) * f),RK) is Element of the carrier of X
(X) . (RK,((X,G) * f)) is set
[RK,((X,G) * f)] is set
{RK,((X,G) * f)} is non empty set
{{RK,((X,G) * f)},{RK}} is non empty set
(X) . [RK,((X,G) * f)] is set
(X,((X,K) * RK1),K1) is Element of the carrier of X
(X) . (K1,((X,K) * RK1)) is set
[K1,((X,K) * RK1)] is set
{K1,((X,K) * RK1)} is non empty set
{K1} is non empty set
{{K1,((X,K) * RK1)},{K1}} is non empty set
(X) . [K1,((X,K) * RK1)] is set
(X,((X,G) * f),RK) \ (X,((X,K) * RK1),K1) is Element of the carrier of X
the InternalDiff of X . ((X,((X,G) * f),RK),(X,((X,K) * RK1),K1)) is Element of the carrier of X
[(X,((X,G) * f),RK),(X,((X,K) * RK1),K1)] is set
{(X,((X,G) * f),RK),(X,((X,K) * RK1),K1)} is non empty set
{(X,((X,G) * f),RK)} is non empty set
{{(X,((X,G) * f),RK),(X,((X,K) * RK1),K1)},{(X,((X,G) * f),RK)}} is non empty set
the InternalDiff of X . [(X,((X,G) * f),RK),(X,((X,K) * RK1),K1)] is set
(X,(X,G),RK) is Element of the carrier of X
(X) . (RK,(X,G)) is set
[RK,(X,G)] is set
{RK,(X,G)} is non empty set
{{RK,(X,G)},{RK}} is non empty set
(X) . [RK,(X,G)] is set
(X,f,(X,(X,G),RK)) is Element of the carrier of X
(X) . ((X,(X,G),RK),f) is set
[(X,(X,G),RK),f] is set
{(X,(X,G),RK),f} is non empty set
{(X,(X,G),RK)} is non empty set
{{(X,(X,G),RK),f},{(X,(X,G),RK)}} is non empty set
(X) . [(X,(X,G),RK),f] is set
(X,f,(X,(X,G),RK)) \ (X,((X,K) * RK1),K1) is Element of the carrier of X
the InternalDiff of X . ((X,f,(X,(X,G),RK)),(X,((X,K) * RK1),K1)) is Element of the carrier of X
[(X,f,(X,(X,G),RK)),(X,((X,K) * RK1),K1)] is set
{(X,f,(X,(X,G),RK)),(X,((X,K) * RK1),K1)} is non empty set
{(X,f,(X,(X,G),RK))} is non empty set
{{(X,f,(X,(X,G),RK)),(X,((X,K) * RK1),K1)},{(X,f,(X,(X,G),RK))}} is non empty set
the InternalDiff of X . [(X,f,(X,(X,G),RK)),(X,((X,K) * RK1),K1)] is set
(X,(X,K),K1) is Element of the carrier of X
(X) . (K1,(X,K)) is set
[K1,(X,K)] is set
{K1,(X,K)} is non empty set
{{K1,(X,K)},{K1}} is non empty set
(X) . [K1,(X,K)] is set
(X,RK1,(X,(X,K),K1)) is Element of the carrier of X
(X) . ((X,(X,K),K1),RK1) is set
[(X,(X,K),K1),RK1] is set
{(X,(X,K),K1),RK1} is non empty set
{(X,(X,K),K1)} is non empty set
{{(X,(X,K),K1),RK1},{(X,(X,K),K1)}} is non empty set
(X) . [(X,(X,K),K1),RK1] is set
(X,f,(X,(X,G),RK)) \ (X,RK1,(X,(X,K),K1)) is Element of the carrier of X
the InternalDiff of X . ((X,f,(X,(X,G),RK)),(X,RK1,(X,(X,K),K1))) is Element of the carrier of X
[(X,f,(X,(X,G),RK)),(X,RK1,(X,(X,K),K1))] is set
{(X,f,(X,(X,G),RK)),(X,RK1,(X,(X,K),K1))} is non empty set
{{(X,f,(X,(X,G),RK)),(X,RK1,(X,(X,K),K1))},{(X,f,(X,(X,G),RK))}} is non empty set
the InternalDiff of X . [(X,f,(X,(X,G),RK)),(X,RK1,(X,(X,K),K1))] is set
I is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,I,RK) is Element of the carrier of X
(X) . (RK,I) is set
[RK,I] is set
{RK,I} is non empty set
{{RK,I},{RK}} is non empty set
(X) . [RK,I] is set
(X,f,(X,I,RK)) is Element of the carrier of X
(X) . ((X,I,RK),f) is set
[(X,I,RK),f] is set
{(X,I,RK),f} is non empty set
{(X,I,RK)} is non empty set
{{(X,I,RK),f},{(X,I,RK)}} is non empty set
(X) . [(X,I,RK),f] is set
(X,f,(X,I,RK)) \ (X,RK1,(X,(X,K),K1)) is Element of the carrier of X
the InternalDiff of X . ((X,f,(X,I,RK)),(X,RK1,(X,(X,K),K1))) is Element of the carrier of X
[(X,f,(X,I,RK)),(X,RK1,(X,(X,K),K1))] is set
{(X,f,(X,I,RK)),(X,RK1,(X,(X,K),K1))} is non empty set
{(X,f,(X,I,RK))} is non empty set
{{(X,f,(X,I,RK)),(X,RK1,(X,(X,K),K1))},{(X,f,(X,I,RK))}} is non empty set
the InternalDiff of X . [(X,f,(X,I,RK)),(X,RK1,(X,(X,K),K1))] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(X,f,(0. X)) is Element of the carrier of X
(X) . ((0. X),f) is set
[(0. X),f] is set
{(0. X),f} is non empty set
{(0. X)} is non empty set
{{(0. X),f},{(0. X)}} is non empty set
(X) . [(0. X),f] is set
(X,f,(0. X)) \ (X,RK1,(X,(X,K),K1)) is Element of the carrier of X
the InternalDiff of X . ((X,f,(0. X)),(X,RK1,(X,(X,K),K1))) is Element of the carrier of X
[(X,f,(0. X)),(X,RK1,(X,(X,K),K1))] is set
{(X,f,(0. X)),(X,RK1,(X,(X,K),K1))} is non empty set
{(X,f,(0. X))} is non empty set
{{(X,f,(0. X)),(X,RK1,(X,(X,K),K1))},{(X,f,(0. X))}} is non empty set
the InternalDiff of X . [(X,f,(0. X)),(X,RK1,(X,(X,K),K1))] is set
(X,K1) is V24() V25() V26() V30() V92() V93() integer ext-real non negative Element of NAT
(X,(X,K1),K1) is Element of the carrier of X
(X) . (K1,(X,K1)) is set
[K1,(X,K1)] is set
{K1,(X,K1)} is non empty set
{{K1,(X,K1)},{K1}} is non empty set
(X) . [K1,(X,K1)] is set
(X,RK1,(X,(X,K1),K1)) is Element of the carrier of X
(X) . ((X,(X,K1),K1),RK1) is set
[(X,(X,K1),K1),RK1] is set
{(X,(X,K1),K1),RK1} is non empty set
{(X,(X,K1),K1)} is non empty set
{{(X,(X,K1),K1),RK1},{(X,(X,K1),K1)}} is non empty set
(X) . [(X,(X,K1),K1),RK1] is set
(X,f,(0. X)) \ (X,RK1,(X,(X,K1),K1)) is Element of the carrier of X
the InternalDiff of X . ((X,f,(0. X)),(X,RK1,(X,(X,K1),K1))) is Element of the carrier of X
[(X,f,(0. X)),(X,RK1,(X,(X,K1),K1))] is set
{(X,f,(0. X)),(X,RK1,(X,(X,K1),K1))} is non empty set
{{(X,f,(0. X)),(X,RK1,(X,(X,K1),K1))},{(X,f,(0. X))}} is non empty set
the InternalDiff of X . [(X,f,(0. X)),(X,RK1,(X,(X,K1),K1))] is set
(X,RK1,(0. X)) is Element of the carrier of X
(X) . ((0. X),RK1) is set
[(0. X),RK1] is set
{(0. X),RK1} is non empty set
{{(0. X),RK1},{(0. X)}} is non empty set
(X) . [(0. X),RK1] is set
(X,f,(0. X)) \ (X,RK1,(0. X)) is Element of the carrier of X
the InternalDiff of X . ((X,f,(0. X)),(X,RK1,(0. X))) is Element of the carrier of X
[(X,f,(0. X)),(X,RK1,(0. X))] is set
{(X,f,(0. X)),(X,RK1,(0. X))} is non empty set
{{(X,f,(0. X)),(X,RK1,(0. X))},{(X,f,(0. X))}} is non empty set
the InternalDiff of X . [(X,f,(0. X)),(X,RK1,(0. X))] is set
(X,RK1,(0. X)) ` is Element of the carrier of X
(0. X) \ (X,RK1,(0. X)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RK1,(0. X))) is Element of the carrier of X
[(0. X),(X,RK1,(0. X))] is set
{(0. X),(X,RK1,(0. X))} is non empty set
{{(0. X),(X,RK1,(0. X))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RK1,(0. X))] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
(X,RI,(RK \ K1)) ` is Element of the carrier of X
(0. X) \ (X,RI,(RK \ K1)) is Element of the carrier of X
the InternalDiff of X . ((0. X),(X,RI,(RK \ K1))) is Element of the carrier of X
[(0. X),(X,RI,(RK \ K1))] is set
{(0. X),(X,RI,(RK \ K1))} is non empty set
{{(0. X),(X,RI,(RK \ K1))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(X,RI,(RK \ K1))] is set
BCK-part X is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : 0. X <= b₁ } is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of G is non empty set
K is Element of the carrier of X
RK is Element of the carrier of X
K \ RK is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (K,RK) is Element of the carrier of X
[K,RK] is set
{K,RK} is non empty set
{K} is non empty set
{{K,RK},{K}} is non empty set
the InternalDiff of X . [K,RK] is set
K1 is Element of the carrier of G
RK1 is Element of the carrier of G
K1 \ RK1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (K1,RK1) is Element of the carrier of G
[K1,RK1] is set
{K1,RK1} is non empty set
{K1} is non empty set
{{K1,RK1},{K1}} is non empty set
the InternalDiff of G . [K1,RK1] is set
the InternalDiff of X || the carrier of G is Relation-like Function-like set
the InternalDiff of X | [: the carrier of G, the carrier of G:] is Relation-like set
( the InternalDiff of X || the carrier of G) . (K1,RK1) is set
( the InternalDiff of X || the carrier of G) . [K1,RK1] is set
X is non empty BCIStr_0
the carrier of X is non empty set
G is non empty BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
the carrier of X --> (0. G) is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total Element of bool [: the carrier of X, the carrier of G:]
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total Element of bool [: the carrier of X, the carrier of G:]
RK is Element of the carrier of X
K1 is Element of the carrier of X
RK \ K1 is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (RK,K1) is Element of the carrier of X
[RK,K1] is set
{RK,K1} is non empty set
{RK} is non empty set
{{RK,K1},{RK}} is non empty set
the InternalDiff of X . [RK,K1] is set
K . (RK \ K1) is Element of the carrier of G
K . RK is Element of the carrier of G
K . K1 is Element of the carrier of G
(K . RK) \ (K . K1) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((K . RK),(K . K1)) is Element of the carrier of G
[(K . RK),(K . K1)] is set
{(K . RK),(K . K1)} is non empty set
{(K . RK)} is non empty set
{{(K . RK),(K . K1)},{(K . RK)}} is non empty set
the InternalDiff of G . [(K . RK),(K . K1)] is set
(0. G) ` is Element of the carrier of G
(0. G) \ (0. G) is Element of the carrier of G
the InternalDiff of G . ((0. G),(0. G)) is Element of the carrier of G
[(0. G),(0. G)] is set
{(0. G),(0. G)} is non empty set
{(0. G)} is non empty set
{{(0. G),(0. G)},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),(0. G)] is set
(K . RK) \ (0. G) is Element of the carrier of G
the InternalDiff of G . ((K . RK),(0. G)) is Element of the carrier of G
[(K . RK),(0. G)] is set
{(K . RK),(0. G)} is non empty set
{{(K . RK),(0. G)},{(K . RK)}} is non empty set
the InternalDiff of G . [(K . RK),(0. G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K . b₁ = 0. G } is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
K . (0. X) is Element of the carrier of G
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
K . ((0. X) `) is Element of the carrier of G
(K . (0. X)) \ (K . (0. X)) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((K . (0. X)),(K . (0. X))) is Element of the carrier of G
[(K . (0. X)),(K . (0. X))] is set
{(K . (0. X)),(K . (0. X))} is non empty set
{(K . (0. X))} is non empty set
{{(K . (0. X)),(K . (0. X))},{(K . (0. X))}} is non empty set
the InternalDiff of G . [(K . (0. X)),(K . (0. X))] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
(X,G,K) is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K . b₁ = 0. G } is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
K . (0. X) is Element of the carrier of G
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is Element of the carrier of X
RK is Element of the carrier of X
K1 is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
K1 . K is Element of the carrier of G
K1 . RK is Element of the carrier of G
(K1 . K) \ (K1 . RK) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((K1 . K),(K1 . RK)) is Element of the carrier of G
[(K1 . K),(K1 . RK)] is set
{(K1 . K),(K1 . RK)} is non empty set
{(K1 . K)} is non empty set
{{(K1 . K),(K1 . RK)},{(K1 . K)}} is non empty set
the InternalDiff of G . [(K1 . K),(K1 . RK)] is set
K \ RK is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (K,RK) is Element of the carrier of X
[K,RK] is set
{K,RK} is non empty set
{K} is non empty set
{{K,RK},{K}} is non empty set
the InternalDiff of X . [K,RK] is set
K1 . (K \ RK) is Element of the carrier of G
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
K1 . (0. X) is Element of the carrier of G
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{(0. G)} is non empty set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
(G,X,K) is non empty set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of G : K . b₁ = 0. X } is set
RK is set
RK1 is Element of the carrier of G
K . RK1 is Element of the carrier of X
K1 is Element of the carrier of G
K . K1 is Element of the carrier of X
K . (0. G) is Element of the carrier of X
RK1 is Element of the carrier of G
K . RK1 is Element of the carrier of X
RK is set
K1 is Element of the carrier of G
K . K1 is Element of the carrier of X
RK is Element of the carrier of G
K1 is Element of the carrier of G
K . RK is Element of the carrier of X
K . K1 is Element of the carrier of X
(K . K1) \ (K . RK) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((K . K1),(K . RK)) is Element of the carrier of X
[(K . K1),(K . RK)] is set
{(K . K1),(K . RK)} is non empty set
{(K . K1)} is non empty set
{{(K . K1),(K . RK)},{(K . K1)}} is non empty set
the InternalDiff of X . [(K . K1),(K . RK)] is set
K1 \ RK is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (K1,RK) is Element of the carrier of G
[K1,RK] is set
{K1,RK} is non empty set
{K1} is non empty set
{{K1,RK},{K1}} is non empty set
the InternalDiff of G . [K1,RK] is set
K . (K1 \ RK) is Element of the carrier of X
(K . RK) \ (K . K1) is Element of the carrier of X
the InternalDiff of X . ((K . RK),(K . K1)) is Element of the carrier of X
[(K . RK),(K . K1)] is set
{(K . RK),(K . K1)} is non empty set
{(K . RK)} is non empty set
{{(K . RK),(K . K1)},{(K . RK)}} is non empty set
the InternalDiff of X . [(K . RK),(K . K1)] is set
RK \ K1 is Element of the carrier of G
the InternalDiff of G . (RK,K1) is Element of the carrier of G
[RK,K1] is set
{RK,K1} is non empty set
{RK} is non empty set
{{RK,K1},{RK}} is non empty set
the InternalDiff of G . [RK,K1] is set
K . (RK \ K1) is Element of the carrier of X
RK is Element of the carrier of G
K . RK is Element of the carrier of X
K1 is Element of the carrier of G
K . K1 is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
K " is Relation-like Function-like set
RK is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
dom K is Element of bool the carrier of G
bool the carrier of G is set
rng RK is Element of bool the carrier of G
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of K is non empty set
[: the carrier of X, the carrier of K:] is set
bool [: the carrier of X, the carrier of K:] is set
[: the carrier of G, the carrier of K:] is set
bool [: the carrier of G, the carrier of K:] is set
RK is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
K1 is Relation-like the carrier of X -defined the carrier of K -valued Function-like non empty V14( the carrier of X) quasi_total (X,K) Element of bool [: the carrier of X, the carrier of K:]
K1 * RK is Relation-like the carrier of G -defined the carrier of K -valued Function-like non empty V14( the carrier of G) quasi_total Element of bool [: the carrier of G, the carrier of K:]
RK1 is Relation-like the carrier of G -defined the carrier of K -valued Function-like non empty V14( the carrier of G) quasi_total Element of bool [: the carrier of G, the carrier of K:]
I is Element of the carrier of G
RI is Element of the carrier of G
I \ RI is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (I,RI) is Element of the carrier of G
[I,RI] is set
{I,RI} is non empty set
{I} is non empty set
{{I,RI},{I}} is non empty set
the InternalDiff of G . [I,RI] is set
RK1 . (I \ RI) is Element of the carrier of K
RK . (I \ RI) is Element of the carrier of X
K1 . (RK . (I \ RI)) is Element of the carrier of K
RK . I is Element of the carrier of X
RK . RI is Element of the carrier of X
(RK . I) \ (RK . RI) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((RK . I),(RK . RI)) is Element of the carrier of X
[(RK . I),(RK . RI)] is set
{(RK . I),(RK . RI)} is non empty set
{(RK . I)} is non empty set
{{(RK . I),(RK . RI)},{(RK . I)}} is non empty set
the InternalDiff of X . [(RK . I),(RK . RI)] is set
K1 . ((RK . I) \ (RK . RI)) is Element of the carrier of K
K1 . (RK . I) is Element of the carrier of K
K1 . (RK . RI) is Element of the carrier of K
(K1 . (RK . I)) \ (K1 . (RK . RI)) is Element of the carrier of K
the InternalDiff of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V14([: the carrier of K, the carrier of K:]) quasi_total Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the InternalDiff of K . ((K1 . (RK . I)),(K1 . (RK . RI))) is Element of the carrier of K
[(K1 . (RK . I)),(K1 . (RK . RI))] is set
{(K1 . (RK . I)),(K1 . (RK . RI))} is non empty set
{(K1 . (RK . I))} is non empty set
{{(K1 . (RK . I)),(K1 . (RK . RI))},{(K1 . (RK . I))}} is non empty set
the InternalDiff of K . [(K1 . (RK . I)),(K1 . (RK . RI))] is set
RK1 . I is Element of the carrier of K
(RK1 . I) \ (K1 . (RK . RI)) is Element of the carrier of K
the InternalDiff of K . ((RK1 . I),(K1 . (RK . RI))) is Element of the carrier of K
[(RK1 . I),(K1 . (RK . RI))] is set
{(RK1 . I),(K1 . (RK . RI))} is non empty set
{(RK1 . I)} is non empty set
{{(RK1 . I),(K1 . (RK . RI))},{(RK1 . I)}} is non empty set
the InternalDiff of K . [(RK1 . I),(K1 . (RK . RI))] is set
RK1 . RI is Element of the carrier of K
(RK1 . I) \ (RK1 . RI) is Element of the carrier of K
the InternalDiff of K . ((RK1 . I),(RK1 . RI)) is Element of the carrier of K
[(RK1 . I),(RK1 . RI)] is set
{(RK1 . I),(RK1 . RI)} is non empty set
{{(RK1 . I),(RK1 . RI)},{(RK1 . I)}} is non empty set
the InternalDiff of K . [(RK1 . I),(RK1 . RI)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
rng K is Element of bool the carrier of X
bool the carrier of X is set
RK is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of RK is non empty set
[: the carrier of G, the carrier of RK:] is set
bool [: the carrier of G, the carrier of RK:] is set
dom K is Element of bool the carrier of G
bool the carrier of G is set
K1 is Relation-like the carrier of G -defined the carrier of RK -valued Function-like non empty V14( the carrier of G) quasi_total Element of bool [: the carrier of G, the carrier of RK:]
RK1 is Element of the carrier of G
K1 . RK1 is Element of the carrier of RK
I is Element of the carrier of G
K1 . I is Element of the carrier of RK
(K1 . RK1) \ (K1 . I) is Element of the carrier of RK
the InternalDiff of RK is Relation-like [: the carrier of RK, the carrier of RK:] -defined the carrier of RK -valued Function-like V14([: the carrier of RK, the carrier of RK:]) quasi_total Element of bool [:[: the carrier of RK, the carrier of RK:], the carrier of RK:]
[: the carrier of RK, the carrier of RK:] is set
[:[: the carrier of RK, the carrier of RK:], the carrier of RK:] is set
bool [:[: the carrier of RK, the carrier of RK:], the carrier of RK:] is set
the InternalDiff of RK . ((K1 . RK1),(K1 . I)) is Element of the carrier of RK
[(K1 . RK1),(K1 . I)] is set
{(K1 . RK1),(K1 . I)} is non empty set
{(K1 . RK1)} is non empty set
{{(K1 . RK1),(K1 . I)},{(K1 . RK1)}} is non empty set
the InternalDiff of RK . [(K1 . RK1),(K1 . I)] is set
K . RK1 is Element of the carrier of X
K . I is Element of the carrier of X
(K . RK1) \ (K . I) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((K . RK1),(K . I)) is Element of the carrier of X
[(K . RK1),(K . I)] is set
{(K . RK1),(K . I)} is non empty set
{(K . RK1)} is non empty set
{{(K . RK1),(K . I)},{(K . RK1)}} is non empty set
the InternalDiff of X . [(K . RK1),(K . I)] is set
RK1 \ I is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (RK1,I) is Element of the carrier of G
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of G . [RK1,I] is set
K1 . (RK1 \ I) is Element of the carrier of RK
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
(G,X,K) is non empty set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of G : K . b₁ = 0. X } is set
RK is set
K1 is Element of the carrier of G
K . K1 is Element of the carrier of X
bool the carrier of G is set
RK is Element of the carrier of G
K1 is Element of the carrier of G
RK \ K1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (RK,K1) is Element of the carrier of G
[RK,K1] is set
{RK,K1} is non empty set
{RK} is non empty set
{{RK,K1},{RK}} is non empty set
the InternalDiff of G . [RK,K1] is set
K . RK is Element of the carrier of X
(K . RK) \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((K . RK),(0. X)) is Element of the carrier of X
[(K . RK),(0. X)] is set
{(K . RK),(0. X)} is non empty set
{(K . RK)} is non empty set
{{(K . RK),(0. X)},{(K . RK)}} is non empty set
the InternalDiff of X . [(K . RK),(0. X)] is set
RK1 is Element of the carrier of G
K . RK1 is Element of the carrier of X
I is Element of the carrier of G
K . I is Element of the carrier of X
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
K . (0. G) is Element of the carrier of X
RK is non empty Ideal of G
K1 is Element of RK
K1 ` is Element of the carrier of G
(0. G) \ K1 is Element of the carrier of G
the InternalDiff of G . ((0. G),K1) is Element of the carrier of G
[(0. G),K1] is set
{(0. G),K1} is non empty set
{(0. G)} is non empty set
{{(0. G),K1},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),K1] is set
K . (K1 `) is Element of the carrier of X
K . K1 is Element of the carrier of X
(K . (0. G)) \ (K . K1) is Element of the carrier of X
the InternalDiff of X . ((K . (0. G)),(K . K1)) is Element of the carrier of X
[(K . (0. G)),(K . K1)] is set
{(K . (0. G)),(K . K1)} is non empty set
{(K . (0. G))} is non empty set
{{(K . (0. G)),(K . K1)},{(K . (0. G))}} is non empty set
the InternalDiff of X . [(K . (0. G)),(K . K1)] is set
(0. X) ` is Element of the carrier of X
(0. X) \ (0. X) is Element of the carrier of X
the InternalDiff of X . ((0. X),(0. X)) is Element of the carrier of X
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(0. X)] is set
RK1 is Element of the carrier of G
K . RK1 is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
(X,G,K) is non empty set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K . b₁ = 0. G } is set
RK is non empty Ideal of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
rng K is Element of bool the carrier of X
bool the carrier of X is set
RK is set
dom K is Element of bool the carrier of G
bool the carrier of G is set
K1 is set
K . K1 is set
RK1 is Element of the carrier of G
K . RK1 is Element of the carrier of X
K1 is Element of the carrier of G
K . K1 is Element of the carrier of X
dom K is Element of bool the carrier of G
bool the carrier of G is set
RK is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
RK is Element of the carrier of G
K . RK is Element of the carrier of X
RK ` is Element of the carrier of G
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
(0. G) \ RK is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((0. G),RK) is Element of the carrier of G
[(0. G),RK] is set
{(0. G),RK} is non empty set
{(0. G)} is non empty set
{{(0. G),RK},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),RK] is set
(RK `) ` is Element of the carrier of G
(0. G) \ (RK `) is Element of the carrier of G
the InternalDiff of G . ((0. G),(RK `)) is Element of the carrier of G
[(0. G),(RK `)] is set
{(0. G),(RK `)} is non empty set
{{(0. G),(RK `)},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),(RK `)] is set
K . ((RK `) `) is Element of the carrier of X
K . (0. G) is Element of the carrier of X
K . ((0. G) \ RK) is Element of the carrier of X
(K . (0. G)) \ (K . ((0. G) \ RK)) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((K . (0. G)),(K . ((0. G) \ RK))) is Element of the carrier of X
[(K . (0. G)),(K . ((0. G) \ RK))] is set
{(K . (0. G)),(K . ((0. G) \ RK))} is non empty set
{(K . (0. G))} is non empty set
{{(K . (0. G)),(K . ((0. G) \ RK))},{(K . (0. G))}} is non empty set
the InternalDiff of X . [(K . (0. G)),(K . ((0. G) \ RK))] is set
(K . (0. G)) \ (K . RK) is Element of the carrier of X
the InternalDiff of X . ((K . (0. G)),(K . RK)) is Element of the carrier of X
[(K . (0. G)),(K . RK)] is set
{(K . (0. G)),(K . RK)} is non empty set
{{(K . (0. G)),(K . RK)},{(K . (0. G))}} is non empty set
the InternalDiff of X . [(K . (0. G)),(K . RK)] is set
(K . (0. G)) \ ((K . (0. G)) \ (K . RK)) is Element of the carrier of X
the InternalDiff of X . ((K . (0. G)),((K . (0. G)) \ (K . RK))) is Element of the carrier of X
[(K . (0. G)),((K . (0. G)) \ (K . RK))] is set
{(K . (0. G)),((K . (0. G)) \ (K . RK))} is non empty set
{{(K . (0. G)),((K . (0. G)) \ (K . RK))},{(K . (0. G))}} is non empty set
the InternalDiff of X . [(K . (0. G)),((K . (0. G)) \ (K . RK))] is set
((K . (0. G)) \ (K . RK)) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ ((K . (0. G)) \ (K . RK)) is Element of the carrier of X
the InternalDiff of X . ((0. X),((K . (0. G)) \ (K . RK))) is Element of the carrier of X
[(0. X),((K . (0. G)) \ (K . RK))] is set
{(0. X),((K . (0. G)) \ (K . RK))} is non empty set
{(0. X)} is non empty set
{{(0. X),((K . (0. G)) \ (K . RK))},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((K . (0. G)) \ (K . RK))] is set
(K . RK) ` is Element of the carrier of X
(0. X) \ (K . RK) is Element of the carrier of X
the InternalDiff of X . ((0. X),(K . RK)) is Element of the carrier of X
[(0. X),(K . RK)] is set
{(0. X),(K . RK)} is non empty set
{{(0. X),(K . RK)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(K . RK)] is set
((K . RK) `) ` is Element of the carrier of X
(0. X) \ ((K . RK) `) is Element of the carrier of X
the InternalDiff of X . ((0. X),((K . RK) `)) is Element of the carrier of X
[(0. X),((K . RK) `)] is set
{(0. X),((K . RK) `)} is non empty set
{{(0. X),((K . RK) `)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),((K . RK) `)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
AtomSet X is non empty Element of bool the carrier of X
bool the carrier of X is set
{ b₁ where b₁ is Element of the carrier of X : b₁ is atom } is set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
AtomSet G is non empty Element of bool the carrier of G
bool the carrier of G is set
{ b₁ where b₁ is Element of the carrier of G : b₁ is atom } is set
K is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
RK is Element of AtomSet X
K . RK is Element of the carrier of G
BranchV RK is non empty Element of bool the carrier of X
{ b₁ where b₁ is Element of the carrier of X : RK <= b₁ } is set
K .: (BranchV RK) is Element of bool the carrier of G
K1 is Element of AtomSet G
BranchV K1 is non empty Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : K1 <= b₁ } is set
RK1 is set
dom K is Element of bool the carrier of X
I is set
K . I is set
RI is Element of the carrier of X
K . RI is Element of the carrier of G
(K . RK) \ (K . RI) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((K . RK),(K . RI)) is Element of the carrier of G
[(K . RK),(K . RI)] is set
{(K . RK),(K . RI)} is non empty set
{(K . RK)} is non empty set
{{(K . RK),(K . RI)},{(K . RK)}} is non empty set
the InternalDiff of G . [(K . RK),(K . RI)] is set
RK \ RI is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (RK,RI) is Element of the carrier of X
[RK,RI] is set
{RK,RI} is non empty set
{RK} is non empty set
{{RK,RI},{RK}} is non empty set
the InternalDiff of X . [RK,RI] is set
K . (RK \ RI) is Element of the carrier of G
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
K . (0. X) is Element of the carrier of G
f is Element of the carrier of X
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
bool the carrier of X is set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is non empty Element of bool the carrier of X
RK is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
RK " K is Element of bool the carrier of G
bool the carrier of G is set
K1 is Element of the carrier of G
RK1 is Element of the carrier of G
K1 \ RK1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (K1,RK1) is Element of the carrier of G
[K1,RK1] is set
{K1,RK1} is non empty set
{K1} is non empty set
{{K1,RK1},{K1}} is non empty set
the InternalDiff of G . [K1,RK1] is set
RK . (K1 \ RK1) is Element of the carrier of X
RK . K1 is Element of the carrier of X
RK . RK1 is Element of the carrier of X
(RK . K1) \ (RK . RK1) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((RK . K1),(RK . RK1)) is Element of the carrier of X
[(RK . K1),(RK . RK1)] is set
{(RK . K1),(RK . RK1)} is non empty set
{(RK . K1)} is non empty set
{{(RK . K1),(RK . RK1)},{(RK . K1)}} is non empty set
the InternalDiff of X . [(RK . K1),(RK . RK1)] is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
RK . (0. G) is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
bool the carrier of X is set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is non empty Element of bool the carrier of X
RK is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
RK " K is Element of bool the carrier of G
bool the carrier of G is set
K1 is non empty Ideal of G
RK1 is Element of K1
RK1 ` is Element of the carrier of G
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
(0. G) \ RK1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((0. G),RK1) is Element of the carrier of G
[(0. G),RK1] is set
{(0. G),RK1} is non empty set
{(0. G)} is non empty set
{{(0. G),RK1},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),RK1] is set
RK . RK1 is Element of the carrier of X
I is Element of the carrier of G
RK . I is Element of the carrier of X
(RK . I) ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ (RK . I) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),(RK . I)) is Element of the carrier of X
[(0. X),(RK . I)] is set
{(0. X),(RK . I)} is non empty set
{(0. X)} is non empty set
{{(0. X),(RK . I)},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),(RK . I)] is set
RK . (0. G) is Element of the carrier of X
(RK . (0. G)) \ (RK . I) is Element of the carrier of X
the InternalDiff of X . ((RK . (0. G)),(RK . I)) is Element of the carrier of X
[(RK . (0. G)),(RK . I)] is set
{(RK . (0. G)),(RK . I)} is non empty set
{(RK . (0. G))} is non empty set
{{(RK . (0. G)),(RK . I)},{(RK . (0. G))}} is non empty set
the InternalDiff of X . [(RK . (0. G)),(RK . I)] is set
I ` is Element of the carrier of G
(0. G) \ I is Element of the carrier of G
the InternalDiff of G . ((0. G),I) is Element of the carrier of G
[(0. G),I] is set
{(0. G),I} is non empty set
{{(0. G),I},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),I] is set
RK . (I `) is Element of the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is non empty Ideal of X
RK is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
RK .: K is Element of bool the carrier of G
bool the carrier of G is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
dom RK is Element of bool the carrier of X
bool the carrier of X is set
RK . (0. X) is Element of the carrier of G
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
K1 is non empty Element of bool the carrier of G
RK1 is Element of the carrier of G
I is Element of the carrier of G
RK1 \ I is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (RK1,I) is Element of the carrier of G
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of G . [RK1,I] is set
RI is set
RK . RI is set
f is Element of the carrier of X
RK . f is Element of the carrier of G
f is set
RK . f is set
y is Element of the carrier of X
f \ y is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (f,y) is Element of the carrier of X
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
the InternalDiff of X . [f,y] is set
x is Element of the carrier of X
(f \ y) \ x is Element of the carrier of X
the InternalDiff of X . ((f \ y),x) is Element of the carrier of X
[(f \ y),x] is set
{(f \ y),x} is non empty set
{(f \ y)} is non empty set
{{(f \ y),x},{(f \ y)}} is non empty set
the InternalDiff of X . [(f \ y),x] is set
f \ ((f \ y) \ x) is Element of the carrier of X
the InternalDiff of X . (f,((f \ y) \ x)) is Element of the carrier of X
[f,((f \ y) \ x)] is set
{f,((f \ y) \ x)} is non empty set
{{f,((f \ y) \ x)},{f}} is non empty set
the InternalDiff of X . [f,((f \ y) \ x)] is set
(f \ y) \ ((f \ y) \ x) is Element of the carrier of X
the InternalDiff of X . ((f \ y),((f \ y) \ x)) is Element of the carrier of X
[(f \ y),((f \ y) \ x)] is set
{(f \ y),((f \ y) \ x)} is non empty set
{{(f \ y),((f \ y) \ x)},{(f \ y)}} is non empty set
the InternalDiff of X . [(f \ y),((f \ y) \ x)] is set
((f \ y) \ ((f \ y) \ x)) \ x is Element of the carrier of X
the InternalDiff of X . (((f \ y) \ ((f \ y) \ x)),x) is Element of the carrier of X
[((f \ y) \ ((f \ y) \ x)),x] is set
{((f \ y) \ ((f \ y) \ x)),x} is non empty set
{((f \ y) \ ((f \ y) \ x))} is non empty set
{{((f \ y) \ ((f \ y) \ x)),x},{((f \ y) \ ((f \ y) \ x))}} is non empty set
the InternalDiff of X . [((f \ y) \ ((f \ y) \ x)),x] is set
(f \ ((f \ y) \ x)) \ y is Element of the carrier of X
the InternalDiff of X . ((f \ ((f \ y) \ x)),y) is Element of the carrier of X
[(f \ ((f \ y) \ x)),y] is set
{(f \ ((f \ y) \ x)),y} is non empty set
{(f \ ((f \ y) \ x))} is non empty set
{{(f \ ((f \ y) \ x)),y},{(f \ ((f \ y) \ x))}} is non empty set
the InternalDiff of X . [(f \ ((f \ y) \ x)),y] is set
((f \ ((f \ y) \ x)) \ y) \ x is Element of the carrier of X
the InternalDiff of X . (((f \ ((f \ y) \ x)) \ y),x) is Element of the carrier of X
[((f \ ((f \ y) \ x)) \ y),x] is set
{((f \ ((f \ y) \ x)) \ y),x} is non empty set
{((f \ ((f \ y) \ x)) \ y)} is non empty set
{{((f \ ((f \ y) \ x)) \ y),x},{((f \ ((f \ y) \ x)) \ y)}} is non empty set
the InternalDiff of X . [((f \ ((f \ y) \ x)) \ y),x] is set
RK . (f \ ((f \ y) \ x)) is Element of the carrier of G
[(f \ ((f \ y) \ x)),(RK . (f \ ((f \ y) \ x)))] is set
{(f \ ((f \ y) \ x)),(RK . (f \ ((f \ y) \ x)))} is non empty set
{{(f \ ((f \ y) \ x)),(RK . (f \ ((f \ y) \ x)))},{(f \ ((f \ y) \ x))}} is non empty set
RK . ((f \ y) \ x) is Element of the carrier of G
(RK . f) \ (RK . ((f \ y) \ x)) is Element of the carrier of G
the InternalDiff of G . ((RK . f),(RK . ((f \ y) \ x))) is Element of the carrier of G
[(RK . f),(RK . ((f \ y) \ x))] is set
{(RK . f),(RK . ((f \ y) \ x))} is non empty set
{(RK . f)} is non empty set
{{(RK . f),(RK . ((f \ y) \ x))},{(RK . f)}} is non empty set
the InternalDiff of G . [(RK . f),(RK . ((f \ y) \ x))] is set
RK . (f \ y) is Element of the carrier of G
RK . x is Element of the carrier of G
(RK . (f \ y)) \ (RK . x) is Element of the carrier of G
the InternalDiff of G . ((RK . (f \ y)),(RK . x)) is Element of the carrier of G
[(RK . (f \ y)),(RK . x)] is set
{(RK . (f \ y)),(RK . x)} is non empty set
{(RK . (f \ y))} is non empty set
{{(RK . (f \ y)),(RK . x)},{(RK . (f \ y))}} is non empty set
the InternalDiff of G . [(RK . (f \ y)),(RK . x)] is set
(RK . f) \ ((RK . (f \ y)) \ (RK . x)) is Element of the carrier of G
the InternalDiff of G . ((RK . f),((RK . (f \ y)) \ (RK . x))) is Element of the carrier of G
[(RK . f),((RK . (f \ y)) \ (RK . x))] is set
{(RK . f),((RK . (f \ y)) \ (RK . x))} is non empty set
{{(RK . f),((RK . (f \ y)) \ (RK . x))},{(RK . f)}} is non empty set
the InternalDiff of G . [(RK . f),((RK . (f \ y)) \ (RK . x))] is set
(RK1 \ I) \ (RK1 \ I) is Element of the carrier of G
the InternalDiff of G . ((RK1 \ I),(RK1 \ I)) is Element of the carrier of G
[(RK1 \ I),(RK1 \ I)] is set
{(RK1 \ I),(RK1 \ I)} is non empty set
{(RK1 \ I)} is non empty set
{{(RK1 \ I),(RK1 \ I)},{(RK1 \ I)}} is non empty set
the InternalDiff of G . [(RK1 \ I),(RK1 \ I)] is set
(RK . f) \ ((RK1 \ I) \ (RK1 \ I)) is Element of the carrier of G
the InternalDiff of G . ((RK . f),((RK1 \ I) \ (RK1 \ I))) is Element of the carrier of G
[(RK . f),((RK1 \ I) \ (RK1 \ I))] is set
{(RK . f),((RK1 \ I) \ (RK1 \ I))} is non empty set
{{(RK . f),((RK1 \ I) \ (RK1 \ I))},{(RK . f)}} is non empty set
the InternalDiff of G . [(RK . f),((RK1 \ I) \ (RK1 \ I))] is set
(RK . f) \ (0. G) is Element of the carrier of G
the InternalDiff of G . ((RK . f),(0. G)) is Element of the carrier of G
[(RK . f),(0. G)] is set
{(RK . f),(0. G)} is non empty set
{{(RK . f),(0. G)},{(RK . f)}} is non empty set
the InternalDiff of G . [(RK . f),(0. G)] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is non empty closed Ideal of X
RK is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
RK .: K is Element of bool the carrier of G
bool the carrier of G is set
K1 is non empty Ideal of G
dom RK is Element of bool the carrier of X
bool the carrier of X is set
RK1 is Element of K1
I is set
RK . I is set
RI is Element of K
RI ` is Element of the carrier of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
(0. X) \ RI is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),RI) is Element of the carrier of X
[(0. X),RI] is set
{(0. X),RI} is non empty set
{(0. X)} is non empty set
{{(0. X),RI},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),RI] is set
RK . (RI `) is Element of the carrier of G
[(RI `),(RK . (RI `))] is set
{(RI `),(RK . (RI `))} is non empty set
{(RI `)} is non empty set
{{(RI `),(RK . (RI `))},{(RI `)}} is non empty set
RK . (0. X) is Element of the carrier of G
RK . RI is Element of the carrier of G
(RK . (0. X)) \ (RK . RI) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((RK . (0. X)),(RK . RI)) is Element of the carrier of G
[(RK . (0. X)),(RK . RI)] is set
{(RK . (0. X)),(RK . RI)} is non empty set
{(RK . (0. X))} is non empty set
{{(RK . (0. X)),(RK . RI)},{(RK . (0. X))}} is non empty set
the InternalDiff of G . [(RK . (0. X)),(RK . RI)] is set
RK1 ` is Element of the carrier of G
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
(0. G) \ RK1 is Element of the carrier of G
the InternalDiff of G . ((0. G),RK1) is Element of the carrier of G
[(0. G),RK1] is set
{(0. G),RK1} is non empty set
{(0. G)} is non empty set
{{(0. G),RK1},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),RK1] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty Ideal of X
K is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,G
X ./. K is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class K is non empty a_partition of the carrier of X
EqClaOp K is Relation-like [:(Class K),(Class K):] -defined Class K -valued Function-like V14([:(Class K),(Class K):]) quasi_total Element of bool [:[:(Class K),(Class K):],(Class K):]
[:(Class K),(Class K):] is set
[:[:(Class K),(Class K):],(Class K):] is set
bool [:[:(Class K),(Class K):],(Class K):] is set
zeroEqC K is Element of Class K
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (K,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class K),(EqClaOp K),(zeroEqC K) #) is strict BCIStr_0
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty Ideal of X
K is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,G
X ./. K is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class K is non empty a_partition of the carrier of X
EqClaOp K is Relation-like [:(Class K),(Class K):] -defined Class K -valued Function-like V14([:(Class K),(Class K):]) quasi_total Element of bool [:[:(Class K),(Class K):],(Class K):]
[:(Class K),(Class K):] is set
[:[:(Class K),(Class K):],(Class K):] is set
bool [:[:(Class K),(Class K):],(Class K):] is set
zeroEqC K is Element of Class K
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (K,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class K),(EqClaOp K),(zeroEqC K) #) is strict BCIStr_0
the carrier of (X ./. K) is non empty set
[: the carrier of X, the carrier of (X ./. K):] is set
bool [: the carrier of X, the carrier of (X ./. K):] is set
RK is Element of the carrier of X
Class (K,RK) is Element of bool the carrier of X
K1 is Element of the carrier of (X ./. K)
RK is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total Element of bool [: the carrier of X, the carrier of (X ./. K):]
K1 is Element of the carrier of X
RK . K1 is Element of the carrier of (X ./. K)
Class (K,K1) is Element of bool the carrier of X
RK1 is Element of the carrier of X
RK . RK1 is Element of the carrier of (X ./. K)
Class (K,RK1) is Element of bool the carrier of X
(RK . K1) \ (RK . RK1) is Element of the carrier of (X ./. K)
the InternalDiff of (X ./. K) is Relation-like [: the carrier of (X ./. K), the carrier of (X ./. K):] -defined the carrier of (X ./. K) -valued Function-like V14([: the carrier of (X ./. K), the carrier of (X ./. K):]) quasi_total Element of bool [:[: the carrier of (X ./. K), the carrier of (X ./. K):], the carrier of (X ./. K):]
[: the carrier of (X ./. K), the carrier of (X ./. K):] is set
[:[: the carrier of (X ./. K), the carrier of (X ./. K):], the carrier of (X ./. K):] is set
bool [:[: the carrier of (X ./. K), the carrier of (X ./. K):], the carrier of (X ./. K):] is set
the InternalDiff of (X ./. K) . ((RK . K1),(RK . RK1)) is Element of the carrier of (X ./. K)
[(RK . K1),(RK . RK1)] is set
{(RK . K1),(RK . RK1)} is non empty set
{(RK . K1)} is non empty set
{{(RK . K1),(RK . RK1)},{(RK . K1)}} is non empty set
the InternalDiff of (X ./. K) . [(RK . K1),(RK . RK1)] is set
K1 \ RK1 is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (K1,RK1) is Element of the carrier of X
[K1,RK1] is set
{K1,RK1} is non empty set
{K1} is non empty set
{{K1,RK1},{K1}} is non empty set
the InternalDiff of X . [K1,RK1] is set
Class (K,(K1 \ RK1)) is Element of bool the carrier of X
RK . (K1 \ RK1) is Element of the carrier of (X ./. K)
K1 is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. K) Element of bool [: the carrier of X, the carrier of (X ./. K):]
RK1 is Element of the carrier of X
K1 . RK1 is Element of the carrier of (X ./. K)
Class (K,RK1) is Element of bool the carrier of X
RK is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. K) Element of bool [: the carrier of X, the carrier of (X ./. K):]
K1 is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. K) Element of bool [: the carrier of X, the carrier of (X ./. K):]
RK1 is Element of the carrier of X
RK . RK1 is Element of the carrier of (X ./. K)
Class (K,RK1) is Element of bool the carrier of X
K1 . RK1 is Element of the carrier of (X ./. K)
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty Ideal of X
K is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,G
X ./. K is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class K is non empty a_partition of the carrier of X
EqClaOp K is Relation-like [:(Class K),(Class K):] -defined Class K -valued Function-like V14([:(Class K),(Class K):]) quasi_total Element of bool [:[:(Class K),(Class K):],(Class K):]
[:(Class K),(Class K):] is set
[:[:(Class K),(Class K):],(Class K):] is set
bool [:[:(Class K),(Class K):],(Class K):] is set
zeroEqC K is Element of Class K
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (K,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class K),(EqClaOp K),(zeroEqC K) #) is strict BCIStr_0
the carrier of (X ./. K) is non empty set
(X,G,K) is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. K) Element of bool [: the carrier of X, the carrier of (X ./. K):]
[: the carrier of X, the carrier of (X ./. K):] is set
bool [: the carrier of X, the carrier of (X ./. K):] is set
RK1 is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of RK1 is non empty set
[: the carrier of X, the carrier of RK1:] is set
bool [: the carrier of X, the carrier of RK1:] is set
I is Relation-like the carrier of X -defined the carrier of RK1 -valued Function-like non empty V14( the carrier of X) quasi_total (X,RK1) Element of bool [: the carrier of X, the carrier of RK1:]
RI is set
f is Element of the carrier of RK1
f is set
Class (K,f) is Element of bool the carrier of X
I . f is set
rng I is Element of bool the carrier of RK1
bool the carrier of RK1 is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is non empty Ideal of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
[: the carrier of (X ./. RK), the carrier of G:] is set
bool [: the carrier of (X ./. RK), the carrier of G:] is set
(X,K,RK) is Relation-like the carrier of X -defined the carrier of (X ./. RK) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. RK) Element of bool [: the carrier of X, the carrier of (X ./. RK):]
[: the carrier of X, the carrier of (X ./. RK):] is set
bool [: the carrier of X, the carrier of (X ./. RK):] is set
K1 is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
(X,G,K1) is non empty set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K1 . b₁ = 0. G } is set
dom (X,K,RK) is Element of bool the carrier of X
I is Element of the carrier of (X ./. RK)
RI is set
Class (RK,RI) is Element of bool the carrier of X
f is Element of the carrier of X
K1 . f is Element of the carrier of G
f is Element of the carrier of G
y is Element of the carrier of X
Class (RK,y) is Element of bool the carrier of X
K1 . y is Element of the carrier of G
[y,f] is set
{y,f} is non empty set
{y} is non empty set
{{y,f},{y}} is non empty set
f \ y is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (f,y) is Element of the carrier of X
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
the InternalDiff of X . [f,y] is set
(K1 . f) \ (K1 . y) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((K1 . f),(K1 . y)) is Element of the carrier of G
[(K1 . f),(K1 . y)] is set
{(K1 . f),(K1 . y)} is non empty set
{(K1 . f)} is non empty set
{{(K1 . f),(K1 . y)},{(K1 . f)}} is non empty set
the InternalDiff of G . [(K1 . f),(K1 . y)] is set
x is Element of the carrier of X
K1 . x is Element of the carrier of G
y \ f is Element of the carrier of X
the InternalDiff of X . (y,f) is Element of the carrier of X
the InternalDiff of X . [y,f] is set
(K1 . y) \ (K1 . f) is Element of the carrier of G
the InternalDiff of G . ((K1 . y),(K1 . f)) is Element of the carrier of G
[(K1 . y),(K1 . f)] is set
{(K1 . y),(K1 . f)} is non empty set
{(K1 . y)} is non empty set
{{(K1 . y),(K1 . f)},{(K1 . y)}} is non empty set
the InternalDiff of G . [(K1 . y),(K1 . f)] is set
x is Element of the carrier of X
K1 . x is Element of the carrier of G
I is Relation-like the carrier of (X ./. RK) -defined the carrier of G -valued Function-like non empty V14( the carrier of (X ./. RK)) quasi_total Element of bool [: the carrier of (X ./. RK), the carrier of G:]
RI is Element of the carrier of (X ./. RK)
f is set
Class (RK,f) is Element of bool the carrier of X
f is Element of the carrier of (X ./. RK)
y is set
Class (RK,y) is Element of bool the carrier of X
RI \ f is Element of the carrier of (X ./. RK)
the InternalDiff of (X ./. RK) is Relation-like [: the carrier of (X ./. RK), the carrier of (X ./. RK):] -defined the carrier of (X ./. RK) -valued Function-like V14([: the carrier of (X ./. RK), the carrier of (X ./. RK):]) quasi_total Element of bool [:[: the carrier of (X ./. RK), the carrier of (X ./. RK):], the carrier of (X ./. RK):]
[: the carrier of (X ./. RK), the carrier of (X ./. RK):] is set
[:[: the carrier of (X ./. RK), the carrier of (X ./. RK):], the carrier of (X ./. RK):] is set
bool [:[: the carrier of (X ./. RK), the carrier of (X ./. RK):], the carrier of (X ./. RK):] is set
the InternalDiff of (X ./. RK) . (RI,f) is Element of the carrier of (X ./. RK)
[RI,f] is set
{RI,f} is non empty set
{RI} is non empty set
{{RI,f},{RI}} is non empty set
the InternalDiff of (X ./. RK) . [RI,f] is set
x is Element of the carrier of X
a is Element of the carrier of X
x \ a is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (x,a) is Element of the carrier of X
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
the InternalDiff of X . [x,a] is set
Class (RK,(x \ a)) is Element of bool the carrier of X
I . f is Element of the carrier of G
K1 . a is Element of the carrier of G
I . RI is Element of the carrier of G
K1 . x is Element of the carrier of G
(I . RI) \ (I . f) is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((I . RI),(I . f)) is Element of the carrier of G
[(I . RI),(I . f)] is set
{(I . RI),(I . f)} is non empty set
{(I . RI)} is non empty set
{{(I . RI),(I . f)},{(I . RI)}} is non empty set
the InternalDiff of G . [(I . RI),(I . f)] is set
K1 . (x \ a) is Element of the carrier of G
I . (RI \ f) is Element of the carrier of G
RI is Relation-like the carrier of (X ./. RK) -defined the carrier of G -valued Function-like non empty V14( the carrier of (X ./. RK)) quasi_total (X ./. RK,G) Element of bool [: the carrier of (X ./. RK), the carrier of G:]
f is set
dom RI is set
f is set
RI . f is set
RI . f is set
dom RI is Element of bool the carrier of (X ./. RK)
bool the carrier of (X ./. RK) is set
y is Element of the carrier of (X ./. RK)
a is set
Class (RK,a) is Element of bool the carrier of X
x is Element of the carrier of (X ./. RK)
x is set
Class (RK,x) is Element of bool the carrier of X
RI . x is Element of the carrier of G
a1 is Element of the carrier of X
K1 . a1 is Element of the carrier of G
RI . y is Element of the carrier of G
Wb is Element of the carrier of X
K1 . Wb is Element of the carrier of G
(K1 . a1) \ (K1 . Wb) is Element of the carrier of G
the InternalDiff of G . ((K1 . a1),(K1 . Wb)) is Element of the carrier of G
[(K1 . a1),(K1 . Wb)] is set
{(K1 . a1),(K1 . Wb)} is non empty set
{(K1 . a1)} is non empty set
{{(K1 . a1),(K1 . Wb)},{(K1 . a1)}} is non empty set
the InternalDiff of G . [(K1 . a1),(K1 . Wb)] is set
a1 \ Wb is Element of the carrier of X
the InternalDiff of X . (a1,Wb) is Element of the carrier of X
[a1,Wb] is set
{a1,Wb} is non empty set
{a1} is non empty set
{{a1,Wb},{a1}} is non empty set
the InternalDiff of X . [a1,Wb] is set
K1 . (a1 \ Wb) is Element of the carrier of G
(K1 . Wb) \ (K1 . a1) is Element of the carrier of G
the InternalDiff of G . ((K1 . Wb),(K1 . a1)) is Element of the carrier of G
[(K1 . Wb),(K1 . a1)] is set
{(K1 . Wb),(K1 . a1)} is non empty set
{(K1 . Wb)} is non empty set
{{(K1 . Wb),(K1 . a1)},{(K1 . Wb)}} is non empty set
the InternalDiff of G . [(K1 . Wb),(K1 . a1)] is set
Wb \ a1 is Element of the carrier of X
the InternalDiff of X . (Wb,a1) is Element of the carrier of X
[Wb,a1] is set
{Wb,a1} is non empty set
{Wb} is non empty set
{{Wb,a1},{Wb}} is non empty set
the InternalDiff of X . [Wb,a1] is set
K1 . (Wb \ a1) is Element of the carrier of G
Class (RK,Wb) is Element of bool the carrier of X
dom K1 is Element of bool the carrier of X
f is set
(X,K,RK) . f is set
dom RI is Element of bool the carrier of (X ./. RK)
bool the carrier of (X ./. RK) is set
rng (X,K,RK) is Element of bool the carrier of (X ./. RK)
RI * (X,K,RK) is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total Element of bool [: the carrier of X, the carrier of G:]
f is set
f is Element of the carrier of X
(X,K,RK) . f is Element of the carrier of (X ./. RK)
Class (RK,f) is Element of bool the carrier of X
K1 . f is set
(X,K,RK) . f is set
RI . ((X,K,RK) . f) is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty Ideal of X
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K1 is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
(X,G,K1) is non empty set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K1 . b₁ = 0. G } is set
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
[: the carrier of (X ./. RK), the carrier of G:] is set
bool [: the carrier of (X ./. RK), the carrier of G:] is set
(X,K,RK) is Relation-like the carrier of X -defined the carrier of (X ./. RK) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. RK) Element of bool [: the carrier of X, the carrier of (X ./. RK):]
[: the carrier of X, the carrier of (X ./. RK):] is set
bool [: the carrier of X, the carrier of (X ./. RK):] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty closed Ideal of X
K is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,G
X ./. K is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class K is non empty a_partition of the carrier of X
EqClaOp K is Relation-like [:(Class K),(Class K):] -defined Class K -valued Function-like V14([:(Class K),(Class K):]) quasi_total Element of bool [:[:(Class K),(Class K):],(Class K):]
[:(Class K),(Class K):] is set
[:[:(Class K),(Class K):],(Class K):] is set
bool [:[:(Class K),(Class K):],(Class K):] is set
zeroEqC K is Element of Class K
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (K,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class K),(EqClaOp K),(zeroEqC K) #) is strict BCIStr_0
(X,G,K) is Relation-like the carrier of X -defined the carrier of (X ./. K) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. K) Element of bool [: the carrier of X, the carrier of (X ./. K):]
the carrier of (X ./. K) is non empty set
[: the carrier of X, the carrier of (X ./. K):] is set
bool [: the carrier of X, the carrier of (X ./. K):] is set
(X,(X ./. K),(X,G,K)) is non empty set
0. (X ./. K) is V47(X ./. K) atom positive nilpotent Element of the carrier of (X ./. K)
the ZeroF of (X ./. K) is Element of the carrier of (X ./. K)
{ b₁ where b₁ is Element of the carrier of X : (X,G,K) . b₁ = 0. (X ./. K) } is set
RK1 is set
I is Element of the carrier of X
(X,G,K) . I is Element of the carrier of (X ./. K)
Class (K,I) is Element of bool the carrier of X
[(0. X),I] is set
{(0. X),I} is non empty set
{(0. X)} is non empty set
{{(0. X),I},{(0. X)}} is non empty set
I \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (I,(0. X)) is Element of the carrier of X
[I,(0. X)] is set
{I,(0. X)} is non empty set
{I} is non empty set
{{I,(0. X)},{I}} is non empty set
the InternalDiff of X . [I,(0. X)] is set
RK1 is set
I is Element of the carrier of X
I \ (0. X) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (I,(0. X)) is Element of the carrier of X
[I,(0. X)] is set
{I,(0. X)} is non empty set
{I} is non empty set
{{I,(0. X)},{I}} is non empty set
the InternalDiff of X . [I,(0. X)] is set
I ` is Element of the carrier of X
(0. X) \ I is Element of the carrier of X
the InternalDiff of X . ((0. X),I) is Element of the carrier of X
[(0. X),I] is set
{(0. X),I} is non empty set
{(0. X)} is non empty set
{{(0. X),I},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),I] is set
Class (K,I) is Element of bool the carrier of X
(X,G,K) . I is Element of the carrier of (X ./. K)
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of K is non empty set
[: the carrier of G, the carrier of K:] is set
bool [: the carrier of G, the carrier of K:] is set
RK is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
rng RK is Element of bool the carrier of X
bool the carrier of X is set
dom RK is Element of bool the carrier of G
bool the carrier of G is set
K1 is Relation-like the carrier of G -defined the carrier of K -valued Function-like non empty V14( the carrier of G) quasi_total Element of bool [: the carrier of G, the carrier of K:]
RK1 is Element of the carrier of G
K1 . RK1 is Element of the carrier of K
I is Element of the carrier of G
K1 . I is Element of the carrier of K
(K1 . RK1) \ (K1 . I) is Element of the carrier of K
the InternalDiff of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V14([: the carrier of K, the carrier of K:]) quasi_total Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the InternalDiff of K . ((K1 . RK1),(K1 . I)) is Element of the carrier of K
[(K1 . RK1),(K1 . I)] is set
{(K1 . RK1),(K1 . I)} is non empty set
{(K1 . RK1)} is non empty set
{{(K1 . RK1),(K1 . I)},{(K1 . RK1)}} is non empty set
the InternalDiff of K . [(K1 . RK1),(K1 . I)] is set
RK . RK1 is Element of the carrier of X
RK . I is Element of the carrier of X
(RK . RK1) \ (RK . I) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((RK . RK1),(RK . I)) is Element of the carrier of X
[(RK . RK1),(RK . I)] is set
{(RK . RK1),(RK . I)} is non empty set
{(RK . RK1)} is non empty set
{{(RK . RK1),(RK . I)},{(RK . RK1)}} is non empty set
the InternalDiff of X . [(RK . RK1),(RK . I)] is set
RK1 \ I is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (RK1,I) is Element of the carrier of G
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of G . [RK1,I] is set
K1 . (RK1 \ I) is Element of the carrier of K
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of G, the carrier of X:] is set
bool [: the carrier of G, the carrier of X:] is set
K is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of K is non empty set
RK is non empty Ideal of G
K1 is Relation-like the carrier of G -defined the carrier of G -valued V14( the carrier of G) quasi_total V77() V79() V84() I-congruence of G,RK
G ./. K1 is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class K1 is non empty a_partition of the carrier of G
EqClaOp K1 is Relation-like [:(Class K1),(Class K1):] -defined Class K1 -valued Function-like V14([:(Class K1),(Class K1):]) quasi_total Element of bool [:[:(Class K1),(Class K1):],(Class K1):]
[:(Class K1),(Class K1):] is set
[:[:(Class K1),(Class K1):],(Class K1):] is set
bool [:[:(Class K1),(Class K1):],(Class K1):] is set
zeroEqC K1 is Element of Class K1
bool the carrier of G is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
Class (K1,(0. G)) is Element of bool the carrier of G
BCIStr_0(# (Class K1),(EqClaOp K1),(zeroEqC K1) #) is strict BCIStr_0
RK1 is Relation-like the carrier of G -defined the carrier of X -valued Function-like non empty V14( the carrier of G) quasi_total (G,X) Element of bool [: the carrier of G, the carrier of X:]
(G,X,RK1) is non empty set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
{ b₁ where b₁ is Element of the carrier of G : RK1 . b₁ = 0. X } is set
rng RK1 is Element of bool the carrier of X
bool the carrier of X is set
the carrier of (G ./. K1) is non empty set
RI is Element of the carrier of (G ./. K1)
f is set
Class (K1,f) is Element of bool the carrier of G
dom RK1 is Element of bool the carrier of G
f is Element of the carrier of G
RK1 . f is Element of the carrier of X
y is Element of the carrier of K
x is Element of the carrier of G
Class (K1,x) is Element of bool the carrier of G
RK1 . x is Element of the carrier of X
[x,f] is set
{x,f} is non empty set
{x} is non empty set
{{x,f},{x}} is non empty set
f \ x is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (f,x) is Element of the carrier of G
[f,x] is set
{f,x} is non empty set
{f} is non empty set
{{f,x},{f}} is non empty set
the InternalDiff of G . [f,x] is set
(RK1 . f) \ (RK1 . x) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((RK1 . f),(RK1 . x)) is Element of the carrier of X
[(RK1 . f),(RK1 . x)] is set
{(RK1 . f),(RK1 . x)} is non empty set
{(RK1 . f)} is non empty set
{{(RK1 . f),(RK1 . x)},{(RK1 . f)}} is non empty set
the InternalDiff of X . [(RK1 . f),(RK1 . x)] is set
a is Element of the carrier of G
RK1 . a is Element of the carrier of X
x \ f is Element of the carrier of G
the InternalDiff of G . (x,f) is Element of the carrier of G
the InternalDiff of G . [x,f] is set
(RK1 . x) \ (RK1 . f) is Element of the carrier of X
the InternalDiff of X . ((RK1 . x),(RK1 . f)) is Element of the carrier of X
[(RK1 . x),(RK1 . f)] is set
{(RK1 . x),(RK1 . f)} is non empty set
{(RK1 . x)} is non empty set
{{(RK1 . x),(RK1 . f)},{(RK1 . x)}} is non empty set
the InternalDiff of X . [(RK1 . x),(RK1 . f)] is set
a is Element of the carrier of G
RK1 . a is Element of the carrier of X
[: the carrier of (G ./. K1), the carrier of K:] is set
bool [: the carrier of (G ./. K1), the carrier of K:] is set
RI is Relation-like the carrier of (G ./. K1) -defined the carrier of K -valued Function-like non empty V14( the carrier of (G ./. K1)) quasi_total Element of bool [: the carrier of (G ./. K1), the carrier of K:]
[: the carrier of G, the carrier of K:] is set
bool [: the carrier of G, the carrier of K:] is set
f is Element of the carrier of (G ./. K1)
x is set
Class (K1,x) is Element of bool the carrier of G
y is Element of the carrier of (G ./. K1)
a is set
Class (K1,a) is Element of bool the carrier of G
f \ y is Element of the carrier of (G ./. K1)
the InternalDiff of (G ./. K1) is Relation-like [: the carrier of (G ./. K1), the carrier of (G ./. K1):] -defined the carrier of (G ./. K1) -valued Function-like V14([: the carrier of (G ./. K1), the carrier of (G ./. K1):]) quasi_total Element of bool [:[: the carrier of (G ./. K1), the carrier of (G ./. K1):], the carrier of (G ./. K1):]
[: the carrier of (G ./. K1), the carrier of (G ./. K1):] is set
[:[: the carrier of (G ./. K1), the carrier of (G ./. K1):], the carrier of (G ./. K1):] is set
bool [:[: the carrier of (G ./. K1), the carrier of (G ./. K1):], the carrier of (G ./. K1):] is set
the InternalDiff of (G ./. K1) . (f,y) is Element of the carrier of (G ./. K1)
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
the InternalDiff of (G ./. K1) . [f,y] is set
x is Element of the carrier of G
Wb is Element of the carrier of G
x \ Wb is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (x,Wb) is Element of the carrier of G
[x,Wb] is set
{x,Wb} is non empty set
{x} is non empty set
{{x,Wb},{x}} is non empty set
the InternalDiff of G . [x,Wb] is set
Class (K1,(x \ Wb)) is Element of bool the carrier of G
RI . y is Element of the carrier of K
f is Relation-like the carrier of G -defined the carrier of K -valued Function-like non empty V14( the carrier of G) quasi_total (G,K) Element of bool [: the carrier of G, the carrier of K:]
f . Wb is Element of the carrier of K
RI . f is Element of the carrier of K
f . x is Element of the carrier of K
(RI . f) \ (RI . y) is Element of the carrier of K
the InternalDiff of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V14([: the carrier of K, the carrier of K:]) quasi_total Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the InternalDiff of K . ((RI . f),(RI . y)) is Element of the carrier of K
[(RI . f),(RI . y)] is set
{(RI . f),(RI . y)} is non empty set
{(RI . f)} is non empty set
{{(RI . f),(RI . y)},{(RI . f)}} is non empty set
the InternalDiff of K . [(RI . f),(RI . y)] is set
f . (x \ Wb) is Element of the carrier of K
RI . (f \ y) is Element of the carrier of K
f is Relation-like the carrier of (G ./. K1) -defined the carrier of K -valued Function-like non empty V14( the carrier of (G ./. K1)) quasi_total (G ./. K1,K) Element of bool [: the carrier of (G ./. K1), the carrier of K:]
f is set
dom f is set
y is set
f . f is set
f . y is set
dom f is Element of bool the carrier of (G ./. K1)
bool the carrier of (G ./. K1) is set
x is Element of the carrier of (G ./. K1)
x is set
Class (K1,x) is Element of bool the carrier of G
a is Element of the carrier of (G ./. K1)
Wb is set
Class (K1,Wb) is Element of bool the carrier of G
f . a is Element of the carrier of K
b1 is Element of the carrier of G
RK1 . b1 is Element of the carrier of X
f . x is Element of the carrier of K
a1 is Element of the carrier of G
RK1 . a1 is Element of the carrier of X
(RK1 . b1) \ (RK1 . a1) is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((RK1 . b1),(RK1 . a1)) is Element of the carrier of X
[(RK1 . b1),(RK1 . a1)] is set
{(RK1 . b1),(RK1 . a1)} is non empty set
{(RK1 . b1)} is non empty set
{{(RK1 . b1),(RK1 . a1)},{(RK1 . b1)}} is non empty set
the InternalDiff of X . [(RK1 . b1),(RK1 . a1)] is set
b1 \ a1 is Element of the carrier of G
the InternalDiff of G . (b1,a1) is Element of the carrier of G
[b1,a1] is set
{b1,a1} is non empty set
{b1} is non empty set
{{b1,a1},{b1}} is non empty set
the InternalDiff of G . [b1,a1] is set
RK1 . (b1 \ a1) is Element of the carrier of X
(RK1 . a1) \ (RK1 . b1) is Element of the carrier of X
the InternalDiff of X . ((RK1 . a1),(RK1 . b1)) is Element of the carrier of X
[(RK1 . a1),(RK1 . b1)] is set
{(RK1 . a1),(RK1 . b1)} is non empty set
{(RK1 . a1)} is non empty set
{{(RK1 . a1),(RK1 . b1)},{(RK1 . a1)}} is non empty set
the InternalDiff of X . [(RK1 . a1),(RK1 . b1)] is set
a1 \ b1 is Element of the carrier of G
the InternalDiff of G . (a1,b1) is Element of the carrier of G
[a1,b1] is set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
the InternalDiff of G . [a1,b1] is set
RK1 . (a1 \ b1) is Element of the carrier of X
Class (K1,a1) is Element of bool the carrier of G
rng f is Element of bool the carrier of K
bool the carrier of K is set
f is set
dom f is Element of bool the carrier of (G ./. K1)
bool the carrier of (G ./. K1) is set
dom RK1 is Element of bool the carrier of G
y is set
RK1 . y is set
Class (K1,y) is Element of bool the carrier of G
x is Element of the carrier of (G ./. K1)
f . x is Element of the carrier of K
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of G is non empty set
[: the carrier of X, the carrier of G:] is set
bool [: the carrier of X, the carrier of G:] is set
K is non empty Ideal of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
K1 is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total (X,G) Element of bool [: the carrier of X, the carrier of G:]
(X,G,K1) is non empty set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
{ b₁ where b₁ is Element of the carrier of X : K1 . b₁ = 0. G } is set
the carrier of (X ./. RK) is non empty set
[: the carrier of (X ./. RK), the carrier of G:] is set
bool [: the carrier of (X ./. RK), the carrier of G:] is set
(X,K,RK) is Relation-like the carrier of X -defined the carrier of (X ./. RK) -valued Function-like non empty V14( the carrier of X) quasi_total (X,X ./. RK) Element of bool [: the carrier of X, the carrier of (X ./. RK):]
[: the carrier of X, the carrier of (X ./. RK):] is set
bool [: the carrier of X, the carrier of (X ./. RK):] is set
RK1 is Relation-like the carrier of (X ./. RK) -defined the carrier of G -valued Function-like non empty V14( the carrier of (X ./. RK)) quasi_total (X ./. RK,G) Element of bool [: the carrier of (X ./. RK), the carrier of G:]
RK1 * (X,K,RK) is Relation-like the carrier of X -defined the carrier of G -valued Function-like non empty V14( the carrier of X) quasi_total Element of bool [: the carrier of X, the carrier of G:]
I is set
rng K1 is Element of bool the carrier of G
bool the carrier of G is set
dom K1 is Element of bool the carrier of X
RI is set
K1 . RI is set
(X,K,RK) . RI is set
RK1 . ((X,K,RK) . RI) is set
dom (X,K,RK) is Element of bool the carrier of X
rng (X,K,RK) is Element of bool the carrier of (X ./. RK)
bool the carrier of (X ./. RK) is set
rng RK1 is Element of bool the carrier of G
bool the carrier of G is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of G is non empty set
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
bool the carrier of X is set
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
I is set
RI is set
f is Element of the carrier of G
Class (RK,f) is Element of bool the carrier of X
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
[(0. X),(0. X)] is set
{(0. X),(0. X)} is non empty set
{(0. X)} is non empty set
{{(0. X),(0. X)},{(0. X)}} is non empty set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of G is non empty set
K is non empty closed Ideal of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
RK1 is Element of (X,G,K,RK)
I is set
RI is Element of the carrier of G
Class (RK,RI) is Element of bool the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
K1 is Element of (X,G,K,RK)
RK1 is Element of (X,G,K,RK)
I is Element of the carrier of G
Class (RK,I) is Element of bool the carrier of X
[I,K1] is set
{I,K1} is non empty set
{I} is non empty set
{{I,K1},{I}} is non empty set
RI is Element of the carrier of G
Class (RK,RI) is Element of bool the carrier of X
f is Element of the carrier of X
f is Element of the carrier of X
f \ f is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (f,f) is Element of the carrier of X
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the InternalDiff of X . [f,f] is set
Class (RK,(f \ f)) is Element of bool the carrier of X
I \ RI is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (I,RI) is Element of the carrier of G
[I,RI] is set
{I,RI} is non empty set
{{I,RI},{I}} is non empty set
the InternalDiff of G . [I,RI] is set
Class (RK,(I \ RI)) is Element of bool the carrier of X
[RI,RK1] is set
{RI,RK1} is non empty set
{RI} is non empty set
{{RI,RK1},{RI}} is non empty set
y is Element of the carrier of X
x is Element of the carrier of X
y \ x is Element of the carrier of X
the InternalDiff of X . (y,x) is Element of the carrier of X
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
the InternalDiff of X . [y,x] is set
[(f \ f),(y \ x)] is set
{(f \ f),(y \ x)} is non empty set
{(f \ f)} is non empty set
{{(f \ f),(y \ x)},{(f \ f)}} is non empty set
a is Element of (X,G,K,RK)
x is Element of the carrier of X
Wb is Element of the carrier of X
x \ Wb is Element of the carrier of X
the InternalDiff of X . (x,Wb) is Element of the carrier of X
[x,Wb] is set
{x,Wb} is non empty set
{x} is non empty set
{{x,Wb},{x}} is non empty set
the InternalDiff of X . [x,Wb] is set
K1 is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
RK1 is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
I is Element of (X,G,K,RK)
RI is Element of (X,G,K,RK)
K1 . (I,RI) is Element of (X,G,K,RK)
[I,RI] is set
{I,RI} is non empty set
{I} is non empty set
{{I,RI},{I}} is non empty set
K1 . [I,RI] is set
I \ RI is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (I,RI) is Element of the carrier of X
the InternalDiff of X . [I,RI] is set
RK1 . (I,RI) is Element of (X,G,K,RK)
RK1 . [I,RI] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
Class (RK,(0. G)) is Element of bool the carrier of X
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is BCIStr_0
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
K1 is Element of (X,G,K,RK)
RK1 is Element of (X,G,K,RK)
(X,G,K,RK) . (K1,RK1) is Element of (X,G,K,RK)
[K1,RK1] is set
{K1,RK1} is non empty set
{K1} is non empty set
{{K1,RK1},{K1}} is non empty set
(X,G,K,RK) . [K1,RK1] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
K is non empty closed Ideal of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty BCIStr_0
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
K1 is non empty BCIStr_0
the carrier of K1 is non empty set
RK1 is Element of the carrier of K1
I is Element of the carrier of K1
RK1 \ I is Element of the carrier of K1
the InternalDiff of K1 is Relation-like [: the carrier of K1, the carrier of K1:] -defined the carrier of K1 -valued Function-like V14([: the carrier of K1, the carrier of K1:]) quasi_total Element of bool [:[: the carrier of K1, the carrier of K1:], the carrier of K1:]
[: the carrier of K1, the carrier of K1:] is set
[:[: the carrier of K1, the carrier of K1:], the carrier of K1:] is set
bool [:[: the carrier of K1, the carrier of K1:], the carrier of K1:] is set
the InternalDiff of K1 . (RK1,I) is Element of the carrier of K1
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,I] is set
0. K1 is V47(K1) Element of the carrier of K1
the ZeroF of K1 is Element of the carrier of K1
I \ RK1 is Element of the carrier of K1
the InternalDiff of K1 . (I,RK1) is Element of the carrier of K1
[I,RK1] is set
{I,RK1} is non empty set
{I} is non empty set
{{I,RK1},{I}} is non empty set
the InternalDiff of K1 . [I,RK1] is set
RI is Element of (X,G,K,RK)
f is Element of (X,G,K,RK)
f is Element of the carrier of X
y is Element of the carrier of X
f \ y is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (f,y) is Element of the carrier of X
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
the InternalDiff of X . [f,y] is set
y \ f is Element of the carrier of X
the InternalDiff of X . (y,f) is Element of the carrier of X
[y,f] is set
{y,f} is non empty set
{y} is non empty set
{{y,f},{y}} is non empty set
the InternalDiff of X . [y,f] is set
the carrier of K1 is non empty set
RK1 is Element of the carrier of K1
I is Element of the carrier of K1
RI is Element of the carrier of K1
f is Element of (X,G,K,RK)
f is Element of (X,G,K,RK)
y is Element of (X,G,K,RK)
x is Element of the carrier of X
a is Element of the carrier of X
x \ a is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (x,a) is Element of the carrier of X
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
the InternalDiff of X . [x,a] is set
(X,G,K,RK,f,f) is Element of (X,G,K,RK)
(X,G,K,RK) . (f,f) is Element of (X,G,K,RK)
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
(X,G,K,RK) . [f,f] is set
x is Element of the carrier of X
x \ a is Element of the carrier of X
the InternalDiff of X . (x,a) is Element of the carrier of X
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
the InternalDiff of X . [x,a] is set
(X,G,K,RK,y,f) is Element of (X,G,K,RK)
(X,G,K,RK) . (y,f) is Element of (X,G,K,RK)
[y,f] is set
{y,f} is non empty set
{y} is non empty set
{{y,f},{y}} is non empty set
(X,G,K,RK) . [y,f] is set
(x \ a) \ (x \ a) is Element of the carrier of X
the InternalDiff of X . ((x \ a),(x \ a)) is Element of the carrier of X
[(x \ a),(x \ a)] is set
{(x \ a),(x \ a)} is non empty set
{(x \ a)} is non empty set
{{(x \ a),(x \ a)},{(x \ a)}} is non empty set
the InternalDiff of X . [(x \ a),(x \ a)] is set
(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)) is Element of (X,G,K,RK)
(X,G,K,RK) . ((X,G,K,RK,f,f),(X,G,K,RK,y,f)) is Element of (X,G,K,RK)
[(X,G,K,RK,f,f),(X,G,K,RK,y,f)] is set
{(X,G,K,RK,f,f),(X,G,K,RK,y,f)} is non empty set
{(X,G,K,RK,f,f)} is non empty set
{{(X,G,K,RK,f,f),(X,G,K,RK,y,f)},{(X,G,K,RK,f,f)}} is non empty set
(X,G,K,RK) . [(X,G,K,RK,f,f),(X,G,K,RK,y,f)] is set
x \ x is Element of the carrier of X
the InternalDiff of X . (x,x) is Element of the carrier of X
[x,x] is set
{x,x} is non empty set
{{x,x},{x}} is non empty set
the InternalDiff of X . [x,x] is set
(X,G,K,RK,f,y) is Element of (X,G,K,RK)
(X,G,K,RK) . (f,y) is Element of (X,G,K,RK)
[f,y] is set
{f,y} is non empty set
{{f,y},{f}} is non empty set
(X,G,K,RK) . [f,y] is set
((x \ a) \ (x \ a)) \ (x \ x) is Element of the carrier of X
the InternalDiff of X . (((x \ a) \ (x \ a)),(x \ x)) is Element of the carrier of X
[((x \ a) \ (x \ a)),(x \ x)] is set
{((x \ a) \ (x \ a)),(x \ x)} is non empty set
{((x \ a) \ (x \ a))} is non empty set
{{((x \ a) \ (x \ a)),(x \ x)},{((x \ a) \ (x \ a))}} is non empty set
the InternalDiff of X . [((x \ a) \ (x \ a)),(x \ x)] is set
(X,G,K,RK,(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)) is Element of (X,G,K,RK)
(X,G,K,RK) . ((X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)) is Element of (X,G,K,RK)
[(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)] is set
{(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)} is non empty set
{(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f))} is non empty set
{{(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)},{(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f))}} is non empty set
(X,G,K,RK) . [(X,G,K,RK,(X,G,K,RK,f,f),(X,G,K,RK,y,f)),(X,G,K,RK,f,y)] is set
RK1 \ I is Element of the carrier of K1
the InternalDiff of K1 is Relation-like [: the carrier of K1, the carrier of K1:] -defined the carrier of K1 -valued Function-like V14([: the carrier of K1, the carrier of K1:]) quasi_total Element of bool [:[: the carrier of K1, the carrier of K1:], the carrier of K1:]
[: the carrier of K1, the carrier of K1:] is set
[:[: the carrier of K1, the carrier of K1:], the carrier of K1:] is set
bool [:[: the carrier of K1, the carrier of K1:], the carrier of K1:] is set
the InternalDiff of K1 . (RK1,I) is Element of the carrier of K1
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,I] is set
RI \ I is Element of the carrier of K1
the InternalDiff of K1 . (RI,I) is Element of the carrier of K1
[RI,I] is set
{RI,I} is non empty set
{RI} is non empty set
{{RI,I},{RI}} is non empty set
the InternalDiff of K1 . [RI,I] is set
(RK1 \ I) \ (RI \ I) is Element of the carrier of K1
the InternalDiff of K1 . ((RK1 \ I),(RI \ I)) is Element of the carrier of K1
[(RK1 \ I),(RI \ I)] is set
{(RK1 \ I),(RI \ I)} is non empty set
{(RK1 \ I)} is non empty set
{{(RK1 \ I),(RI \ I)},{(RK1 \ I)}} is non empty set
the InternalDiff of K1 . [(RK1 \ I),(RI \ I)] is set
RK1 \ RI is Element of the carrier of K1
the InternalDiff of K1 . (RK1,RI) is Element of the carrier of K1
[RK1,RI] is set
{RK1,RI} is non empty set
{{RK1,RI},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,RI] is set
((RK1 \ I) \ (RI \ I)) \ (RK1 \ RI) is Element of the carrier of K1
the InternalDiff of K1 . (((RK1 \ I) \ (RI \ I)),(RK1 \ RI)) is Element of the carrier of K1
[((RK1 \ I) \ (RI \ I)),(RK1 \ RI)] is set
{((RK1 \ I) \ (RI \ I)),(RK1 \ RI)} is non empty set
{((RK1 \ I) \ (RI \ I))} is non empty set
{{((RK1 \ I) \ (RI \ I)),(RK1 \ RI)},{((RK1 \ I) \ (RI \ I))}} is non empty set
the InternalDiff of K1 . [((RK1 \ I) \ (RI \ I)),(RK1 \ RI)] is set
0. K1 is V47(K1) Element of the carrier of K1
the ZeroF of K1 is Element of the carrier of K1
RK1 is Element of the carrier of K1
I is Element of the carrier of K1
RK1 \ I is Element of the carrier of K1
the InternalDiff of K1 . (RK1,I) is Element of the carrier of K1
[RK1,I] is set
{RK1,I} is non empty set
{RK1} is non empty set
{{RK1,I},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,I] is set
RI is Element of the carrier of K1
(RK1 \ I) \ RI is Element of the carrier of K1
the InternalDiff of K1 . ((RK1 \ I),RI) is Element of the carrier of K1
[(RK1 \ I),RI] is set
{(RK1 \ I),RI} is non empty set
{(RK1 \ I)} is non empty set
{{(RK1 \ I),RI},{(RK1 \ I)}} is non empty set
the InternalDiff of K1 . [(RK1 \ I),RI] is set
RK1 \ RI is Element of the carrier of K1
the InternalDiff of K1 . (RK1,RI) is Element of the carrier of K1
[RK1,RI] is set
{RK1,RI} is non empty set
{{RK1,RI},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,RI] is set
(RK1 \ RI) \ I is Element of the carrier of K1
the InternalDiff of K1 . ((RK1 \ RI),I) is Element of the carrier of K1
[(RK1 \ RI),I] is set
{(RK1 \ RI),I} is non empty set
{(RK1 \ RI)} is non empty set
{{(RK1 \ RI),I},{(RK1 \ RI)}} is non empty set
the InternalDiff of K1 . [(RK1 \ RI),I] is set
((RK1 \ I) \ RI) \ ((RK1 \ RI) \ I) is Element of the carrier of K1
the InternalDiff of K1 . (((RK1 \ I) \ RI),((RK1 \ RI) \ I)) is Element of the carrier of K1
[((RK1 \ I) \ RI),((RK1 \ RI) \ I)] is set
{((RK1 \ I) \ RI),((RK1 \ RI) \ I)} is non empty set
{((RK1 \ I) \ RI)} is non empty set
{{((RK1 \ I) \ RI),((RK1 \ RI) \ I)},{((RK1 \ I) \ RI)}} is non empty set
the InternalDiff of K1 . [((RK1 \ I) \ RI),((RK1 \ RI) \ I)] is set
f is Element of (X,G,K,RK)
f is Element of (X,G,K,RK)
y is Element of (X,G,K,RK)
x is Element of the carrier of X
x is Element of the carrier of X
x \ x is Element of the carrier of X
the InternalDiff of X . (x,x) is Element of the carrier of X
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
the InternalDiff of X . [x,x] is set
(X,G,K,RK,f,y) is Element of (X,G,K,RK)
(X,G,K,RK) . (f,y) is Element of (X,G,K,RK)
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
(X,G,K,RK) . [f,y] is set
a is Element of the carrier of X
(x \ x) \ a is Element of the carrier of X
the InternalDiff of X . ((x \ x),a) is Element of the carrier of X
[(x \ x),a] is set
{(x \ x),a} is non empty set
{(x \ x)} is non empty set
{{(x \ x),a},{(x \ x)}} is non empty set
the InternalDiff of X . [(x \ x),a] is set
(X,G,K,RK,(X,G,K,RK,f,y),f) is Element of (X,G,K,RK)
(X,G,K,RK) . ((X,G,K,RK,f,y),f) is Element of (X,G,K,RK)
[(X,G,K,RK,f,y),f] is set
{(X,G,K,RK,f,y),f} is non empty set
{(X,G,K,RK,f,y)} is non empty set
{{(X,G,K,RK,f,y),f},{(X,G,K,RK,f,y)}} is non empty set
(X,G,K,RK) . [(X,G,K,RK,f,y),f] is set
x \ a is Element of the carrier of X
the InternalDiff of X . (x,a) is Element of the carrier of X
[x,a] is set
{x,a} is non empty set
{{x,a},{x}} is non empty set
the InternalDiff of X . [x,a] is set
(X,G,K,RK,f,f) is Element of (X,G,K,RK)
(X,G,K,RK) . (f,f) is Element of (X,G,K,RK)
[f,f] is set
{f,f} is non empty set
{{f,f},{f}} is non empty set
(X,G,K,RK) . [f,f] is set
(x \ a) \ x is Element of the carrier of X
the InternalDiff of X . ((x \ a),x) is Element of the carrier of X
[(x \ a),x] is set
{(x \ a),x} is non empty set
{(x \ a)} is non empty set
{{(x \ a),x},{(x \ a)}} is non empty set
the InternalDiff of X . [(x \ a),x] is set
(X,G,K,RK,(X,G,K,RK,f,f),y) is Element of (X,G,K,RK)
(X,G,K,RK) . ((X,G,K,RK,f,f),y) is Element of (X,G,K,RK)
[(X,G,K,RK,f,f),y] is set
{(X,G,K,RK,f,f),y} is non empty set
{(X,G,K,RK,f,f)} is non empty set
{{(X,G,K,RK,f,f),y},{(X,G,K,RK,f,f)}} is non empty set
(X,G,K,RK) . [(X,G,K,RK,f,f),y] is set
((x \ a) \ x) \ ((x \ x) \ a) is Element of the carrier of X
the InternalDiff of X . (((x \ a) \ x),((x \ x) \ a)) is Element of the carrier of X
[((x \ a) \ x),((x \ x) \ a)] is set
{((x \ a) \ x),((x \ x) \ a)} is non empty set
{((x \ a) \ x)} is non empty set
{{((x \ a) \ x),((x \ x) \ a)},{((x \ a) \ x)}} is non empty set
the InternalDiff of X . [((x \ a) \ x),((x \ x) \ a)] is set
(X,G,K,RK,(X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)) is Element of (X,G,K,RK)
(X,G,K,RK) . ((X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)) is Element of (X,G,K,RK)
[(X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)] is set
{(X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)} is non empty set
{(X,G,K,RK,(X,G,K,RK,f,f),y)} is non empty set
{{(X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)},{(X,G,K,RK,(X,G,K,RK,f,f),y)}} is non empty set
(X,G,K,RK) . [(X,G,K,RK,(X,G,K,RK,f,f),y),(X,G,K,RK,(X,G,K,RK,f,y),f)] is set
RK1 is Element of the carrier of K1
RK1 \ RK1 is Element of the carrier of K1
the InternalDiff of K1 . (RK1,RK1) is Element of the carrier of K1
[RK1,RK1] is set
{RK1,RK1} is non empty set
{RK1} is non empty set
{{RK1,RK1},{RK1}} is non empty set
the InternalDiff of K1 . [RK1,RK1] is set
I is Element of (X,G,K,RK)
RI is Element of the carrier of X
RI \ RI is Element of the carrier of X
the InternalDiff of X . (RI,RI) is Element of the carrier of X
[RI,RI] is set
{RI,RI} is non empty set
{RI} is non empty set
{{RI,RI},{RI}} is non empty set
the InternalDiff of X . [RI,RI] is set
(X,G,K,RK,I,I) is Element of (X,G,K,RK)
(X,G,K,RK) . (I,I) is Element of (X,G,K,RK)
[I,I] is set
{I,I} is non empty set
{I} is non empty set
{{I,I},{I}} is non empty set
(X,G,K,RK) . [I,I] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
K is non empty closed Ideal of X
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty BCIStr_0
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
K is non empty closed Ideal of X
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
(X,G,K,RK) is non empty Element of bool the carrier of X
bool the carrier of X is set
the carrier of G is non empty set
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
the carrier of (X,G,K,RK) is non empty set
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X || the carrier of (X,G,K,RK) is Relation-like Function-like set
[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] is set
the InternalDiff of X | [: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] is Relation-like set
dom the InternalDiff of X is Relation-like the carrier of X -defined the carrier of X -valued Element of bool [: the carrier of X, the carrier of X:]
bool [: the carrier of X, the carrier of X:] is set
dom ( the InternalDiff of X || the carrier of (X,G,K,RK)) is set
[: the carrier of X, the carrier of X:] /\ [: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] is set
I is non empty set
[:I,I:] is set
f is set
y is set
( the InternalDiff of X || the carrier of (X,G,K,RK)) . y is set
x is set
a is set
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
x is Element of (X,G,K,RK)
Wb is Element of (X,G,K,RK)
a1 is Element of the carrier of X
b1 is Element of the carrier of X
a1 \ b1 is Element of the carrier of X
the InternalDiff of X . (a1,b1) is Element of the carrier of X
[a1,b1] is set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
the InternalDiff of X . [a1,b1] is set
(X,G,K,RK,x,Wb) is Element of (X,G,K,RK)
(X,G,K,RK) . (x,Wb) is Element of (X,G,K,RK)
[x,Wb] is set
{x,Wb} is non empty set
{x} is non empty set
{{x,Wb},{x}} is non empty set
(X,G,K,RK) . [x,Wb] is set
0. (X,G,K,RK) is V47((X,G,K,RK)) atom positive nilpotent Element of the carrier of (X,G,K,RK)
the ZeroF of (X,G,K,RK) is Element of the carrier of (X,G,K,RK)
[f,(0. (X,G,K,RK))] is set
{f,(0. (X,G,K,RK))} is non empty set
{f} is non empty set
{{f,(0. (X,G,K,RK))},{f}} is non empty set
( the InternalDiff of X || the carrier of (X,G,K,RK)) . [f,(0. (X,G,K,RK))] is set
y is Element of the carrier of X
x is Element of the carrier of X
y \ x is Element of the carrier of X
the InternalDiff of X . (y,x) is Element of the carrier of X
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
the InternalDiff of X . [y,x] is set
y is set
( the InternalDiff of X || the carrier of (X,G,K,RK)) . y is set
x is set
( the InternalDiff of X || the carrier of (X,G,K,RK)) . x is set
rng ( the InternalDiff of X || the carrier of (X,G,K,RK)) is set
[:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):] is set
bool [:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):] is set
the InternalDiff of (X,G,K,RK) is Relation-like [: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] -defined the carrier of (X,G,K,RK) -valued Function-like V14([: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):]) quasi_total Element of bool [:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):]
x is Element of the carrier of (X,G,K,RK)
a is Element of the carrier of (X,G,K,RK)
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
f is Relation-like [: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] -defined the carrier of (X,G,K,RK) -valued Function-like V14([: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):]) quasi_total Element of bool [:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):]
f . (x,a) is Element of the carrier of (X,G,K,RK)
f . [x,a] is set
x is Element of the carrier of X
Wb is Element of the carrier of X
x \ Wb is Element of the carrier of X
the InternalDiff of X . (x,Wb) is Element of the carrier of X
[x,Wb] is set
{x,Wb} is non empty set
{x} is non empty set
{{x,Wb},{x}} is non empty set
the InternalDiff of X . [x,Wb] is set
the InternalDiff of (X,G,K,RK) . (x,a) is Element of the carrier of (X,G,K,RK)
the InternalDiff of (X,G,K,RK) . [x,a] is set
0. (X,G,K,RK) is V47((X,G,K,RK)) atom positive nilpotent Element of the carrier of (X,G,K,RK)
the ZeroF of (X,G,K,RK) is Element of the carrier of (X,G,K,RK)
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of G is non empty set
K is non empty closed Ideal of X
the carrier of G /\ K is Element of bool the carrier of X
bool the carrier of X is set
K1 is Element of the carrier of G
RK1 is Element of the carrier of G
K1 \ RK1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (K1,RK1) is Element of the carrier of G
[K1,RK1] is set
{K1,RK1} is non empty set
{K1} is non empty set
{{K1,RK1},{K1}} is non empty set
the InternalDiff of G . [K1,RK1] is set
I is Element of the carrier of X
RI is Element of the carrier of X
I \ RI is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (I,RI) is Element of the carrier of X
[I,RI] is set
{I,RI} is non empty set
{I} is non empty set
{{I,RI},{I}} is non empty set
the InternalDiff of X . [I,RI] is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
K1 is set
bool the carrier of G is set
K1 is non empty Ideal of G
RK1 is Element of K1
RK1 ` is Element of the carrier of G
(0. G) \ RK1 is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . ((0. G),RK1) is Element of the carrier of G
[(0. G),RK1] is set
{(0. G),RK1} is non empty set
{(0. G)} is non empty set
{{(0. G),RK1},{(0. G)}} is non empty set
the InternalDiff of G . [(0. G),RK1] is set
I is Element of the carrier of X
I ` is Element of the carrier of X
(0. X) \ I is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . ((0. X),I) is Element of the carrier of X
[(0. X),I] is set
{(0. X),I} is non empty set
{(0. X)} is non empty set
{{(0. X),I},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),I] is set
X is non empty being_B being_C being_I being_BCI-4 BCIStr_0
the carrier of X is non empty set
G is non empty being_B being_C being_I being_BCI-4 SubAlgebra of X
the carrier of G is non empty set
K is non empty closed Ideal of X
the carrier of G /\ K is Element of bool the carrier of X
bool the carrier of X is set
RK is Relation-like the carrier of X -defined the carrier of X -valued V14( the carrier of X) quasi_total V77() V79() V84() I-congruence of X,K
(X,G,K,RK) is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
(X,G,K,RK) is non empty Element of bool the carrier of X
X ./. RK is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK is non empty a_partition of the carrier of X
EqClaOp RK is Relation-like [:(Class RK),(Class RK):] -defined Class RK -valued Function-like V14([:(Class RK),(Class RK):]) quasi_total Element of bool [:[:(Class RK),(Class RK):],(Class RK):]
[:(Class RK),(Class RK):] is set
[:[:(Class RK),(Class RK):],(Class RK):] is set
bool [:[:(Class RK),(Class RK):],(Class RK):] is set
zeroEqC RK is Element of Class RK
0. X is V47(X) atom positive nilpotent Element of the carrier of X
the ZeroF of X is Element of the carrier of X
Class (RK,(0. X)) is Element of bool the carrier of X
BCIStr_0(# (Class RK),(EqClaOp RK),(zeroEqC RK) #) is strict BCIStr_0
the carrier of (X ./. RK) is non empty set
{ (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
union { (Class (RK,b₁)) where b₁ is Element of the carrier of G : Class (RK,b₁) in the carrier of (X ./. RK) } is set
(X,G,K,RK) is Relation-like [:(X,G,K,RK),(X,G,K,RK):] -defined (X,G,K,RK) -valued Function-like V14([:(X,G,K,RK),(X,G,K,RK):]) quasi_total Element of bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):]
[:(X,G,K,RK),(X,G,K,RK):] is set
[:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
bool [:[:(X,G,K,RK),(X,G,K,RK):],(X,G,K,RK):] is set
(X,G,K,RK) is Element of (X,G,K,RK)
BCIStr_0(# (X,G,K,RK),(X,G,K,RK),(X,G,K,RK) #) is strict BCIStr_0
the carrier of (X,G,K,RK) is non empty set
K1 is non empty Ideal of (X,G,K,RK)
RK1 is Relation-like the carrier of (X,G,K,RK) -defined the carrier of (X,G,K,RK) -valued V14( the carrier of (X,G,K,RK)) quasi_total V77() V79() V84() I-congruence of (X,G,K,RK),K1
(X,G,K,RK) ./. RK1 is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RK1 is non empty a_partition of the carrier of (X,G,K,RK)
EqClaOp RK1 is Relation-like [:(Class RK1),(Class RK1):] -defined Class RK1 -valued Function-like V14([:(Class RK1),(Class RK1):]) quasi_total Element of bool [:[:(Class RK1),(Class RK1):],(Class RK1):]
[:(Class RK1),(Class RK1):] is set
[:[:(Class RK1),(Class RK1):],(Class RK1):] is set
bool [:[:(Class RK1),(Class RK1):],(Class RK1):] is set
zeroEqC RK1 is Element of Class RK1
bool the carrier of (X,G,K,RK) is set
0. (X,G,K,RK) is V47((X,G,K,RK)) atom positive nilpotent Element of the carrier of (X,G,K,RK)
the ZeroF of (X,G,K,RK) is Element of the carrier of (X,G,K,RK)
Class (RK1,(0. (X,G,K,RK))) is Element of bool the carrier of (X,G,K,RK)
BCIStr_0(# (Class RK1),(EqClaOp RK1),(zeroEqC RK1) #) is strict BCIStr_0
I is non empty Ideal of G
RI is Relation-like the carrier of G -defined the carrier of G -valued V14( the carrier of G) quasi_total V77() V79() V84() I-congruence of G,I
G ./. RI is non empty strict being_B being_C being_I being_BCI-4 BCIStr_0
Class RI is non empty a_partition of the carrier of G
EqClaOp RI is Relation-like [:(Class RI),(Class RI):] -defined Class RI -valued Function-like V14([:(Class RI),(Class RI):]) quasi_total Element of bool [:[:(Class RI),(Class RI):],(Class RI):]
[:(Class RI),(Class RI):] is set
[:[:(Class RI),(Class RI):],(Class RI):] is set
bool [:[:(Class RI),(Class RI):],(Class RI):] is set
zeroEqC RI is Element of Class RI
bool the carrier of G is set
0. G is V47(G) atom positive nilpotent Element of the carrier of G
the ZeroF of G is Element of the carrier of G
Class (RI,(0. G)) is Element of bool the carrier of G
BCIStr_0(# (Class RI),(EqClaOp RI),(zeroEqC RI) #) is strict BCIStr_0
f is set
f is Element of the carrier of G
Class (RK,f) is Element of bool the carrier of X
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the carrier of ((X,G,K,RK) ./. RK1) is non empty set
f is Element of the carrier of G
Class (RK1,f) is Element of bool the carrier of (X,G,K,RK)
y is Element of the carrier of ((X,G,K,RK) ./. RK1)
[: the carrier of G, the carrier of ((X,G,K,RK) ./. RK1):] is set
bool [: the carrier of G, the carrier of ((X,G,K,RK) ./. RK1):] is set
f is Relation-like the carrier of G -defined the carrier of ((X,G,K,RK) ./. RK1) -valued Function-like non empty V14( the carrier of G) quasi_total Element of bool [: the carrier of G, the carrier of ((X,G,K,RK) ./. RK1):]
f is Element of the carrier of G
y is Element of the carrier of G
Class (RK1,f) is Element of bool the carrier of (X,G,K,RK)
Class (RK1,y) is Element of bool the carrier of (X,G,K,RK)
x is Element of Class RK1
f . f is Element of the carrier of ((X,G,K,RK) ./. RK1)
Wb is Element of Class RK1
f . y is Element of the carrier of ((X,G,K,RK) ./. RK1)
(f . f) \ (f . y) is Element of the carrier of ((X,G,K,RK) ./. RK1)
the InternalDiff of ((X,G,K,RK) ./. RK1) is Relation-like [: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):] -defined the carrier of ((X,G,K,RK) ./. RK1) -valued Function-like V14([: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):]) quasi_total Element of bool [:[: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):], the carrier of ((X,G,K,RK) ./. RK1):]
[: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):] is set
[:[: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):], the carrier of ((X,G,K,RK) ./. RK1):] is set
bool [:[: the carrier of ((X,G,K,RK) ./. RK1), the carrier of ((X,G,K,RK) ./. RK1):], the carrier of ((X,G,K,RK) ./. RK1):] is set
the InternalDiff of ((X,G,K,RK) ./. RK1) . ((f . f),(f . y)) is Element of the carrier of ((X,G,K,RK) ./. RK1)
[(f . f),(f . y)] is set
{(f . f),(f . y)} is non empty set
{(f . f)} is non empty set
{{(f . f),(f . y)},{(f . f)}} is non empty set
the InternalDiff of ((X,G,K,RK) ./. RK1) . [(f . f),(f . y)] is set
a1 is Element of the carrier of (X,G,K,RK)
b1 is Element of the carrier of (X,G,K,RK)
a1 \ b1 is Element of the carrier of (X,G,K,RK)
the InternalDiff of (X,G,K,RK) is Relation-like [: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] -defined the carrier of (X,G,K,RK) -valued Function-like V14([: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):]) quasi_total Element of bool [:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):]
[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):] is set
[:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):] is set
bool [:[: the carrier of (X,G,K,RK), the carrier of (X,G,K,RK):], the carrier of (X,G,K,RK):] is set
the InternalDiff of (X,G,K,RK) . (a1,b1) is Element of the carrier of (X,G,K,RK)
[a1,b1] is set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
the InternalDiff of (X,G,K,RK) . [a1,b1] is set
Class (RK1,(a1 \ b1)) is Element of bool the carrier of (X,G,K,RK)
x is Element of the carrier of X
a is Element of the carrier of X
x \ a is Element of the carrier of X
the InternalDiff of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V14([: the carrier of X, the carrier of X:]) quasi_total Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the InternalDiff of X . (x,a) is Element of the carrier of X
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
the InternalDiff of X . [x,a] is set
f \ y is Element of the carrier of G
the InternalDiff of G is Relation-like [: the carrier of G, the carrier of G:] -defined the carrier of G -valued Function-like V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:], the carrier of G:]
[: the carrier of G, the carrier of G:] is set
[:[: the carrier of G, the carrier of G:], the carrier of G:] is set
bool [:[: the carrier of G, the carrier of G:], the carrier of G:] is set
the InternalDiff of G . (f,y) is Element of the carrier of G
[f,y] is set
{f,y} is non empty set
{f} is non empty set
{{f,y},{f}} is non empty set
the InternalDiff of G . [f,y] is set
Class (RK1,(f \ y)) is Element of bool the carrier of (X,G,K,RK)
f . (f \ y) is Element of the carrier of ((X,G,K,RK) ./. RK1)
f is Relation-like the carrier of G -defined the carrier of ((X,G,K,RK) ./. RK1) -valued Function-like non empty V14( the carrier of G) quasi_total (G,(X,G,K,RK) ./. RK1) Element of bool [: the carrier of G, the carrier of ((X,G,K,RK) ./. RK1):]
(G,((X,G,K,RK) ./. RK1),f) is non empty set
0. ((X,G,K,RK) ./. RK1) is V47((X,G,K,RK) ./. RK1) atom positive nilpotent Element of the carrier of ((X,G,K,RK) ./. RK1)
the ZeroF of ((X,G,K,RK) ./. RK1) is Element of the carrier of ((X,G,K,RK) ./. RK1)
{ b₁ where b₁ is Element of the carrier of G : f . b₁ = 0. ((X,G,K,RK) ./. RK1) } is set
x is set
a is Element of the carrier of G
f . a is Element of the carrier of ((X,G,K,RK) ./. RK1)
x is Element of the carrier of X
Class (RK,x) is Element of bool the carrier of X
[x,(0. X)] is set
{x,(0. X)} is non empty set
{x} is non empty set
{{x,(0. X)},{x}} is non empty set
x \ (0. X) is Element of the carrier of X
the InternalDiff of X . (x,(0. X)) is Element of the carrier of X
the InternalDiff of X . [x,(0. X)] is set
x is set
a is Element of the carrier of X
a \ (0. X) is Element of the carrier of X
the InternalDiff of X . (a,(0. X)) is Element of the carrier of X
[a,(0. X)] is set
{a,(0. X)} is non empty set
{a} is non empty set
{{a,(0. X)},{a}} is non empty set
the InternalDiff of X . [a,(0. X)] is set
a ` is Element of the carrier of X
(0. X) \ a is Element of the carrier of X
the InternalDiff of X . ((0. X),a) is Element of the carrier of X
[(0. X),a] is set
{(0. X),a} is non empty set
{(0. X)} is non empty set
{{(0. X),a},{(0. X)}} is non empty set
the InternalDiff of X . [(0. X),a] is set
Class (RK,a) is Element of bool the carrier of X
Class (RK1,x) is Element of bool the carrier of (X,G,K,RK)
Class (RK1,(0. X)) is Element of bool the carrier of (X,G,K,RK)
f . x is set
y is set
rng f is Element of bool the carrier of ((X,G,K,RK) ./. RK1)
bool the carrier of ((X,G,K,RK) ./. RK1) is set
x is set
Class (RK1,x) is Element of bool the carrier of (X,G,K,RK)
a is Element of the carrier of G
Class (RK,a) is Element of bool the carrier of X
Class (RK1,a) is Element of bool the carrier of (X,G,K,RK)
f . a is Element of the carrier of ((X,G,K,RK) ./. RK1)
dom f is Element of bool the carrier of G