let E be set ; :: thesis: for A being Subset of (E ^omega )
for k, l being Nat st k <= l holds
(A * ) ^^ (A |^ k,l) = A |^.. k
let A be Subset of (E ^omega ); :: thesis: for k, l being Nat st k <= l holds
(A * ) ^^ (A |^ k,l) = A |^.. k
let k, l be Nat; :: thesis: ( k <= l implies (A * ) ^^ (A |^ k,l) = A |^.. k )
assume k <= l ; :: thesis: (A * ) ^^ (A |^ k,l) = A |^.. k
then (A |^.. 0 ) ^^ (A |^ k,l) = A |^.. (0 + k) by Th33;
hence (A * ) ^^ (A |^ k,l) = A |^.. k by Th11; :: thesis: verum