let C1 be non empty AltGraph ; :: thesis: for C2 being non empty reflexive AltGraph
for o2 being Object of C2
for m being Morphism of o2,o2
for o, o9 being Object of C1
for f being Morphism of o,o9 st <^o,o9^> <> {} holds
(C1 --> m) . f = m
let C2 be non empty reflexive AltGraph ; :: thesis: for o2 being Object of C2
for m being Morphism of o2,o2
for o, o9 being Object of C1
for f being Morphism of o,o9 st <^o,o9^> <> {} holds
(C1 --> m) . f = m
let o2 be Object of C2; :: thesis: for m being Morphism of o2,o2
for o, o9 being Object of C1
for f being Morphism of o,o9 st <^o,o9^> <> {} holds
(C1 --> m) . f = m
A1: <^o2,o2^> <> {} by ALTCAT_2:def 7;
let m be Morphism of o2,o2; :: thesis: for o, o9 being Object of C1
for f being Morphism of o,o9 st <^o,o9^> <> {} holds
(C1 --> m) . f = m
set F = C1 --> m;
let o, o9 be Object of C1; :: thesis: for f being Morphism of o,o9 st <^o,o9^> <> {} holds
(C1 --> m) . f = m
let f be Morphism of o,o9; :: thesis: ( <^o,o9^> <> {} implies (C1 --> m) . f = m )
assume A2: <^o,o9^> <> {} ; :: thesis: (C1 --> m) . f = m
then <^((C1 --> m) . o9),((C1 --> m) . o)^> <> {} by Def19;
hence (C1 --> m) . f = (Morph-Map ((C1 --> m),o,o9)) . f by A2, Def16
.= m by A1, A2, Th24 ;
:: thesis: verum