reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th3:
  m >= 2 & n >= 2 implies m*n is composite
  proof
    assume
A1: 2 <= m;
    assume
A2: 2 <= n;
    then 2*2 <= m*n by A1,XREAL_1:66;
    hence 2 <= m*n by XXREAL_0:2;
    ex N being Nat st N divides m*n & N <> 1 & N <> m*n
    proof
      take m;
      thus m divides m*n;
      thus m <> 1 by A1;
      assume m = m*n;
      then m*n = m*1;
      then n = 1 by A1,XCMPLX_1:5;
      hence thesis by A2;
    end;
    hence thesis;
  end;
