let f be Function; :: thesis: for x being object st x in dom f holds
(uncurry <*f*>) . (1,x) = f . x
let x be object ; :: thesis: ( x in dom f implies (uncurry <*f*>) . (1,x) = f . x )
assume A1: x in dom f ; :: thesis: (uncurry <*f*>) . (1,x) = f . x
len <*f*> = 1 by FINSEQ_1:40;
then A2: 1 in dom <*f*> by FINSEQ_3:25;
<*f*> . 1 = f ;
hence (uncurry <*f*>) . (1,x) = f . x by A1, A2, FUNCT_5:38; :: thesis: verum