let i, k be Nat; :: thesis: for f being Element of REAL *
for r being Real holds dom ((f,i) := (k,r)) = dom f
let f be Element of REAL * ; :: thesis: for r being Real holds dom ((f,i) := (k,r)) = dom f
let r be Real; :: thesis: dom ((f,i) := (k,r)) = dom f
set fik = (f,i) := k;
thus dom ((f,i) := (k,r)) = dom ((f,i) := k) by FUNCT_7:30
.= dom f by FUNCT_7:30 ; :: thesis: verum