let D be non empty set ; :: thesis: for p1, p2, p3, q being Element of D holds Replace (<*p1,p2,p3*>,2,q) = <*p1,q,p3*>
let p1, p2, p3, q be Element of D; :: thesis: Replace (<*p1,p2,p3*>,2,q) = <*p1,q,p3*>
set f = <*p1,p2,p3*>;
A1: 2 -' 1 = (1 + 1) -' 1
.= 1 by NAT_D:34 ;
A2: len <*p1,p2,p3*> = 2 + 1 by FINSEQ_1:45;
len <*p1,p2,p3*> = 3 by FINSEQ_1:45;
then Replace (<*p1,p2,p3*>,2,q) = ((<*p1,p2,p3*> | (2 -' 1)) ^ <*q*>) ^ (<*p1,p2,p3*> /^ 2) by Def1
.= ((<*p1,p2,p3*> | 1) ^ <*q*>) ^ <*(<*p1,p2,p3*> . 3)*> by A1, A2, FINSEQ_5:30
.= ((<*p1,p2,p3*> | 1) ^ <*q*>) ^ <*p3*>
.= (<*(<*p1,p2,p3*> . 1)*> ^ <*q*>) ^ <*p3*> by FINSEQ_5:20
.= (<*p1*> ^ <*q*>) ^ <*p3*> ;
hence Replace (<*p1,p2,p3*>,2,q) = <*p1,q,p3*> ; :: thesis: verum