let E be set ; :: thesis: for A being Subset of (E ^omega )
for k being Nat holds (A |^.. k) ^^ (A ? ) = A |^.. k
let A be Subset of (E ^omega ); :: thesis: for k being Nat holds (A |^.. k) ^^ (A ? ) = A |^.. k
let k be Nat; :: thesis: (A |^.. k) ^^ (A ? ) = A |^.. k
thus (A |^.. k) ^^ (A ? ) = (A |^.. k) ^^ (A |^ 0 ,1) by FLANG_2:79
.= A |^.. (k + 0 ) by Th33
.= A |^.. k ; :: thesis: verum