
theorem Th53:
for X be non empty set, F be without_+infty-valued FinSequence of
  Funcs(X,ExtREAL), n be Nat st n in dom F holds (F/.n)"{+infty} = {}
proof
   let X be non empty set, F be without_+infty-valued
   FinSequence of Funcs(X,ExtREAL), n be Nat;
   assume A1: n in dom F; then
   F.n is without+infty by DEF10; then
   not +infty in rng(F.n) by MESFUNC5:def 4; then
   not +infty in rng(F/.n) by A1,PARTFUN1:def 6;
   hence (F/.n)"{+infty} = {} by FUNCT_1:72;
end;
