let i, k be Nat; :: thesis: for f being Element of REAL *
for r being Real st i <> k & i in dom f holds
((f,i) := (k,r)) . i = k
let f be Element of REAL * ; :: thesis: for r being Real st i <> k & i in dom f holds
((f,i) := (k,r)) . i = k
let r be Real; :: thesis: ( i <> k & i in dom f implies ((f,i) := (k,r)) . i = k )
assume that
A1: i <> k and
A2: i in dom f ; :: thesis: ((f,i) := (k,r)) . i = k
set fik = (f,i) := k;
thus ((f,i) := (k,r)) . i = ((f,i) := k) . i by A1, FUNCT_7:32
.= k by A2, FUNCT_7:31 ; :: thesis: verum