let D be non empty set ; :: thesis: for p1, p2, q being Element of D holds Replace (<*p1,p2*>,2,q) = <*p1,q*>
let p1, p2, q be Element of D; :: thesis: Replace (<*p1,p2*>,2,q) = <*p1,q*>
set f = <*p1,p2*>;
A1: 2 -' 1 = (1 + 1) -' 1
.= 1 by NAT_D:34 ;
2 <= len <*p1,p2*> by FINSEQ_1:44;
then Replace (<*p1,p2*>,2,q) = ((<*p1,p2*> | (2 -' 1)) ^ <*q*>) ^ (<*p1,p2*> /^ 2) by Def1
.= ((<*p1,p2*> | 1) ^ <*q*>) ^ (<*p1,p2*> /^ (len <*p1,p2*>)) by A1, FINSEQ_1:44
.= ((<*p1,p2*> | 1) ^ <*q*>) ^ {} by RFINSEQ:27
.= (<*(<*p1,p2*> . 1)*> ^ <*q*>) ^ {} by FINSEQ_5:20
.= <*(<*p1,p2*> . 1)*> ^ <*q*> by FINSEQ_1:34
.= <*p1*> ^ <*q*> ;
hence Replace (<*p1,p2*>,2,q) = <*p1,q*> ; :: thesis: verum