let E be set ; :: thesis: for A being Subset of (E ^omega )
for k being Nat holds (A |^.. k) ^^ (A ? ) = (A ? ) ^^ (A |^.. k)
let A be Subset of (E ^omega ); :: thesis: for k being Nat holds (A |^.. k) ^^ (A ? ) = (A ? ) ^^ (A |^.. k)
let k be Nat; :: thesis: (A |^.. k) ^^ (A ? ) = (A ? ) ^^ (A |^.. k)
thus (A |^.. k) ^^ (A ? ) = (A |^.. k) ^^ (A |^ 0 ,1) by FLANG_2:79
.= (A |^ 0 ,1) ^^ (A |^.. k) by Th25
.= (A ? ) ^^ (A |^.. k) by FLANG_2:79 ; :: thesis: verum