let D be non empty set ; :: thesis: for p1, p2, p3 being Element of D holds Swap <*p1,p2,p3*>,1,2 = <*p2,p1,p3*>
let p1, p2, p3 be Element of D; :: thesis: Swap <*p1,p2,p3*>,1,2 = <*p2,p1,p3*>
set f = <*p1,p2,p3*>;
A1: len <*p1,p2,p3*> = 3 by FINSEQ_1:62;
then 1 in dom <*p1,p2,p3*> by FINSEQ_3:27;
then A2: <*p1,p2,p3*> /. 1 = <*p1,p2,p3*> . 1 by PARTFUN1:def 8
.= p1 by FINSEQ_1:62 ;
2 in dom <*p1,p2,p3*> by A1, FINSEQ_3:27;
then A3: <*p1,p2,p3*> /. 2 = <*p1,p2,p3*> . 2 by PARTFUN1:def 8
.= p2 by FINSEQ_1:62 ;
Swap <*p1,p2,p3*>,1,2 = Replace (Replace <*p1,p2,p3*>,1,(<*p1,p2,p3*> /. 2)),2,(<*p1,p2,p3*> /. 1) by A1, Def2
.= Replace <*p2,p2,p3*>,2,(<*p1,p2,p3*> /. 1) by A3, Th17 ;
hence Swap <*p1,p2,p3*>,1,2 = <*p2,p1,p3*> by A2, Th18; :: thesis: verum