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