let D be non empty set ; for p1, p2, q being Element of D holds Replace (<*p1,p2*>,1,q) = <*q,p2*>
let p1, p2, q be Element of D; Replace (<*p1,p2*>,1,q) = <*q,p2*>
set f = <*p1,p2*>;
A1:
len <*p1,p2*> = 2
by FINSEQ_1:44;
1 + 1 = len <*p1,p2*>
by FINSEQ_1:44;
then A3:
<*p1,p2*> /^ 1 = <*(<*p1,p2*> . 2)*>
by FINSEQ_5:30;
Replace (<*p1,p2*>,1,q) =
((<*p1,p2*> | (1 -' 1)) ^ <*q*>) ^ (<*p1,p2*> /^ 1)
by A1, Def1
.=
((<*p1,p2*> | 0) ^ <*q*>) ^ (<*p1,p2*> /^ 1)
by XREAL_1:232
.=
({} ^ <*q*>) ^ <*p2*>
by A3
.=
<*q*> ^ <*p2*>
by FINSEQ_1:34
;
hence
Replace (<*p1,p2*>,1,q) = <*q,p2*>
; verum