let D be non empty set ; :: thesis: for p1, p2, p3 being Element of D st p1 <> p2 holds
Rotate <*p1,p2,p3*>,p2 = <*p2,p3,p2*>
let p1, p2, p3 be Element of D; :: thesis: ( p1 <> p2 implies Rotate <*p1,p2,p3*>,p2 = <*p2,p3,p2*> )
assume A1: p1 <> p2 ; :: thesis: Rotate <*p1,p2,p3*>,p2 = <*p2,p3,p2*>
rng <*p1,p2,p3*> = {p1,p2,p3} by Lm2;
then p2 in rng <*p1,p2,p3*> by ENUMSET1:def 1;
hence Rotate <*p1,p2,p3*>,p2 = (<*p1,p2,p3*> :- p2) ^ ((<*p1,p2,p3*> -: p2) /^ 1) by Def2
.= <*p2,p3*> ^ ((<*p1,p2,p3*> -: p2) /^ 1) by A1, Th58
.= <*p2,p3*> ^ (<*p1,p2*> /^ 1) by A1, Th54
.= <*p2,p3*> ^ <*p2*> by Th50
.= <*p2,p3,p2*> by FINSEQ_1:60 ;
:: thesis: verum