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

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