
theorem Th7:
for X be non empty set, A1,A2 be Subset of X, r1,r2 be Real holds
 <*chi(r1,A1,X),chi(r2,A2,X)*> is summable FinSequence of Funcs(X,ExtREAL)
proof
   let X be non empty set, A1,A2 be Subset of X, r1,r2 be Real;
   reconsider f1=chi(r1,A1,X), f2=chi(r2,A2,X) as Element of Funcs(X,ExtREAL)
     by FUNCT_2:8;
   reconsider F = <*f1,f2*> as FinSequence of Funcs(X,ExtREAL);
A1:f1 is without+infty without-infty & f2 is without+infty without-infty
     by Th4;
A2:dom F = {1,2} by FINSEQ_1:92;
   now let n be Nat;
    assume n in dom F; then
    n = 1 or n = 2 by A2,TARSKI:def 2;
    hence F.n is without-infty by A1;
   end; then
   F is without_-infty-valued;
   hence <*chi(r1,A1,X),chi(r2,A2,X)*> is
     summable FinSequence of Funcs(X,ExtREAL);
end;
