let E be set ; :: thesis: for A, B being Subset of (E ^omega)
for n being Nat holds (A |^ n) \/ (B |^ n) c= (A \/ B) |^ n
let A, B be Subset of (E ^omega); :: thesis: for n being Nat holds (A |^ n) \/ (B |^ n) c= (A \/ B) |^ n
let n be Nat; :: thesis: (A |^ n) \/ (B |^ n) c= (A \/ B) |^ n
( A |^ n c= (A \/ B) |^ n & B |^ n c= (A \/ B) |^ n ) by Th37, XBOOLE_1:7;
hence (A |^ n) \/ (B |^ n) c= (A \/ B) |^ n by XBOOLE_1:8; :: thesis: verum