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 FLANG_1:26
.= (A |^ 1) ^^ (A |^ (m,n)) by Th35
.= A ^^ (A |^ (m,n)) by FLANG_1:26 ; :: thesis: verum