 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;

theorem Th12:
  for i,j,h being natural Number holds i <= j implies i <= j + h
proof
  let i,j,h be natural Number;
  assume i <= j; then
A1: i + h <= j + h by XREAL_1:7;
  0 <= h by Th2;
  then i + 0 <= i + h by XREAL_1:7;
  hence thesis by A1,XXREAL_0:2;
end;
