let E be set ; :: thesis: for A being Subset of (E ^omega)
for m, n being Nat holds (A |^ m) ^^ (A |^ n) = (A |^ n) ^^ (A |^ m)
let A be Subset of (E ^omega); :: thesis: for m, n being Nat holds (A |^ m) ^^ (A |^ n) = (A |^ n) ^^ (A |^ m)
let m, n be Nat; :: thesis: (A |^ m) ^^ (A |^ n) = (A |^ n) ^^ (A |^ m)
thus (A |^ m) ^^ (A |^ n) = A |^ (m + n) by FLANG_1:33
.= (A |^ n) ^^ (A |^ m) by FLANG_1:33 ; :: thesis: verum