let E be set ; :: thesis: for A being Subset of (E ^omega)
for m, n being Nat holds (A |^ (m,n)) ^^ (A +) = (A +) ^^ (A |^ (m,n))
let A be Subset of (E ^omega); :: thesis: for m, n being Nat holds (A |^ (m,n)) ^^ (A +) = (A +) ^^ (A |^ (m,n))
let m, n be Nat; :: thesis: (A |^ (m,n)) ^^ (A +) = (A +) ^^ (A |^ (m,n))
thus (A |^ (m,n)) ^^ (A +) = (A |^ (m,n)) ^^ (A |^.. 1) by Th50
.= (A |^.. 1) ^^ (A |^ (m,n)) by Th25
.= (A +) ^^ (A |^ (m,n)) by Th50 ; :: thesis: verum