let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of C st a is initial & dom f = a & cod f = b holds
init (a,b) = f
let a, b be Object of C; :: thesis: for f being Morphism of C st a is initial & dom f = a & cod f = b holds
init (a,b) = f
let f be Morphism of C; :: thesis: ( a is initial & dom f = a & cod f = b implies init (a,b) = f )
assume that
A1: a is initial and
A2: ( dom f = a & cod f = b ) ; :: thesis: init (a,b) = f
consider h being Morphism of a,b such that
A3: for g being Morphism of a,b holds h = g by A1;
f is Morphism of a,b by A2, CAT_1:4;
hence f = h by A3
.= init (a,b) by A3 ;
:: thesis: verum