let x be set ; :: thesis: for f, g, h being Function st x in dom f holds
( <*f*> .. 1,x = f . x & <*f,g*> .. 1,x = f . x & <*f,g,h*> .. 1,x = f . x )
let f, g, h be Function; :: thesis: ( x in dom f implies ( <*f*> .. 1,x = f . x & <*f,g*> .. 1,x = f . x & <*f,g,h*> .. 1,x = f . x ) )
( <*f*> . 1 = f & <*f,g*> . 1 = f & <*f,g,h*> . 1 = f & 1 in Seg 1 & 1 in Seg 2 & 1 in Seg 3 & dom <*f*> = Seg 1 & dom <*f,g*> = Seg 2 & dom <*f,g,h*> = Seg 3 ) by ENUMSET1:def 1, FINSEQ_1:4, FINSEQ_1:61, FINSEQ_1:62, FINSEQ_1:def 8, FINSEQ_3:1, FINSEQ_3:29, FINSEQ_3:30, TARSKI:def 1, TARSKI:def 2;
hence ( x in dom f implies ( <*f*> .. 1,x = f . x & <*f,g*> .. 1,x = f . x & <*f,g,h*> .. 1,x = f . x ) ) by FUNCT_5:45; :: thesis: verum