let D be non empty set ; for f being FinSequence of D
for i being Nat holds Swap (f,i,i) = f
let f be FinSequence of D; for i being Nat holds Swap (f,i,i) = f
let i be Nat; Swap (f,i,i) = f
reconsider i = i as Element of NAT by ORDINAL1:def 12;
per cases
( ( 1 <= i & i <= len f ) or not 1 <= i or not i <= len f )
;
suppose
( 1
<= i &
i <= len f )
;
Swap (f,i,i) = fthen Swap (
f,
i,
i) =
Replace (
(Replace (f,i,(f /. i))),
i,
(f /. i))
by Def2
.=
Replace (
f,
i,
(f /. i))
by FUNCT_7:38
;
hence
Swap (
f,
i,
i)
= f
by FUNCT_7:38;
verum end; end;