let X be non empty set ; :: thesis: for F being Functional_Sequence of X,ExtREAL st F is additive & F is with_the_same_dom holds
Partial_Sums F is with_the_same_dom
let F be Functional_Sequence of X,ExtREAL; :: thesis: ( F is additive & F is with_the_same_dom implies Partial_Sums F is with_the_same_dom )
assume that
A1: F is additive and
A2: F is with_the_same_dom ; :: thesis: Partial_Sums F is with_the_same_dom
let n, m be Nat; :: according to MESFUNC8:def 2 :: thesis: dom ((Partial_Sums F) . n) = dom ((Partial_Sums F) . m)
dom ((Partial_Sums F) . n) = dom (F . 0) by A1, A2, Th29;
hence dom ((Partial_Sums F) . n) = dom ((Partial_Sums F) . m) by A1, A2, Th29; :: thesis: verum