
theorem Th40:
  for X be non empty set, F be Functional_Sequence of X,ExtREAL
    st F is with_the_same_dom holds -F is with_the_same_dom
proof
    let X be non empty set, F be Functional_Sequence of X,ExtREAL;
    assume A1: F is with_the_same_dom;
    now let n,m be Nat;
     (-F).n = -(F.n) & (-F).m = -(F.m) by Th37; then
     dom((-F).n) = dom(F.n) & dom((-F).m) = dom(F.m) by MESFUNC1:def 7;
     hence dom((-F).n) = dom((-F).m) by A1,MESFUNC8:def 2;
    end;
    hence -F is with_the_same_dom by MESFUNC8:def 2;
end;
