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 + 1)

let A be Subset of (E ^omega); :: thesis: for k, l being Nat st k <= l holds

(A +) ^^ (A |^ (k,l)) = A |^.. (k + 1)

let k, l be Nat; :: thesis: ( k <= l implies (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1) )

assume k <= l ; :: thesis: (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1)

then (A |^.. 1) ^^ (A |^ (k,l)) = A |^.. (1 + k) by Th33;

hence (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1) by Th50; :: thesis: verum

for k, l being Nat st k <= l holds

(A +) ^^ (A |^ (k,l)) = A |^.. (k + 1)

let A be Subset of (E ^omega); :: thesis: for k, l being Nat st k <= l holds

(A +) ^^ (A |^ (k,l)) = A |^.. (k + 1)

let k, l be Nat; :: thesis: ( k <= l implies (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1) )

assume k <= l ; :: thesis: (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1)

then (A |^.. 1) ^^ (A |^ (k,l)) = A |^.. (1 + k) by Th33;

hence (A +) ^^ (A |^ (k,l)) = A |^.. (k + 1) by Th50; :: thesis: verum