let C be para-functional category; :: thesis: for a, b being object of C st <^a,b^> <> {} holds
for f being Morphism of a,b holds
( dom f = the_carrier_of a & rng f c= the_carrier_of b )
let a, b be object of C; :: thesis: ( <^a,b^> <> {} implies for f being Morphism of a,b holds
( dom f = the_carrier_of a & rng f c= the_carrier_of b ) )
assume A1: <^a,b^> <> {} ; :: thesis: for f being Morphism of a,b holds
( dom f = the_carrier_of a & rng f c= the_carrier_of b )
let f be Morphism of a,b; :: thesis: ( dom f = the_carrier_of a & rng f c= the_carrier_of b )
( <^a,b^> c= Funcs (the_carrier_of a),(the_carrier_of b) & f in <^a,b^> ) by A1, Th34;
hence ( dom f = the_carrier_of a & rng f c= the_carrier_of b ) by FUNCT_2:169; :: thesis: verum