let T be 1-sorted ; :: thesis: for S being non empty 1-sorted
for f being Function of T,S st rng f = [#] S & f is one-to-one holds
(f " ) " = f
let S be non empty 1-sorted ; :: thesis: for f being Function of T,S st rng f = [#] S & f is one-to-one holds
(f " ) " = f
let f be Function of T,S; :: thesis: ( rng f = [#] S & f is one-to-one implies (f " ) " = f )
assume that
A1: rng f = [#] S and
A2: f is one-to-one ; :: thesis: (f " ) " = f
f = (f " ) " by A2, FUNCT_1:65;
then A3: f = (f " ) " by A1, A2, Def4;
rng (f " ) = [#] T by A1, A2, Th62;
hence (f " ) " = f by A1, A2, A3, Def4, Th63; :: thesis: verum