reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r for Real;
reserve p,p1,p2 for Prime;

theorem Th15:
  n divides 36 implies n = 1 or n = 2 or n = 3 or n = 4 or n = 6 or n = 9
                    or n = 12 or n = 18 or n = 36
  proof
    assume n divides 36;
    then n divides 6*6;
    then consider a,b such that
A1: a divides 6 & b divides 6 and
A2: n = a*b by Lem1;
    (a = 1 or a = 2 or a = 3 or a = 6) &
    (b = 1 or b = 2 or b = 3 or b = 6) by A1,Th10;
    hence thesis by A2;
  end;
