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

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