
theorem Th65:
  for F be FinSequence of ExtREAL, k be Nat holds
     (F is without-infty implies F/^k is without-infty)
   & (F is without+infty implies F/^k is without+infty)
proof
    let F be FinSequence of ExtREAL, k be Nat;
    hereby assume F is without-infty; then
A1:  not -infty in rng F by MESFUNC5:def 3;
     rng(F/^k) c= rng F by FINSEQ_5:33;
     hence F/^k is without-infty by A1,MESFUNC5:def 3;
    end;
    assume F is without+infty; then
A2: not +infty in rng F by MESFUNC5:def 4;
    rng(F/^k) c= rng F by FINSEQ_5:33;
    hence F/^k is without+infty by A2,MESFUNC5:def 4;
end;
