begin
theorem Th1:
theorem Th2:
theorem
theorem Th4:
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
theorem Th10:
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
theorem
theorem Th16:
theorem Th17:
theorem
theorem Th19:
theorem
theorem Th21:
theorem Th22:
theorem Th23:
theorem Th24:
theorem Th25:
theorem Th26:
theorem
theorem Th28:
theorem
theorem Th30:
theorem Th31:
theorem
theorem
theorem
theorem Th35:
theorem Th36:
theorem
:: deftheorem Def1 defines ComplMap YELLOW_7:def 1 :
theorem
theorem
for
S,
T being non
empty RelStr for
f being
set holds
( (
f is
Function of
S,
T implies
f is
Function of
(S opp ),
T ) & (
f is
Function of
(S opp ),
T implies
f is
Function of
S,
T ) & (
f is
Function of
S,
T implies
f is
Function of
S,
(T opp ) ) & (
f is
Function of
S,
(T opp ) implies
f is
Function of
S,
T ) & (
f is
Function of
S,
T implies
f is
Function of
(S opp ),
(T opp ) ) & (
f is
Function of
(S opp ),
(T opp ) implies
f is
Function of
S,
T ) ) ;
theorem
theorem
theorem Th42:
theorem
for
S,
T being non
empty RelStr for
f being
set holds
( (
f is
Connection of
S,
T implies
f is
Connection of
S ~ ,
T ) & (
f is
Connection of
S ~ ,
T implies
f is
Connection of
S,
T ) & (
f is
Connection of
S,
T implies
f is
Connection of
S,
T ~ ) & (
f is
Connection of
S,
T ~ implies
f is
Connection of
S,
T ) & (
f is
Connection of
S,
T implies
f is
Connection of
S ~ ,
T ~ ) & (
f is
Connection of
S ~ ,
T ~ implies
f is
Connection of
S,
T ) )
theorem
theorem Th45:
theorem
theorem Th47:
theorem Th48:
theorem Th49:
theorem Th50:
theorem