
theorem lemmonus:
for a,b being Nat st a <= b holds a -' 1 <= b -' 1
proof
let a,b be Nat;
assume AS: a <= b;
per cases;
suppose a = 0;
  then a - 1 = -1;
  hence thesis by XREAL_0:def 2;
  end;
suppose a > 0;
 then a -'1 = a - 1 & b -' 1 = b - 1 by AS,XREAL_0:def 2;
 hence thesis by AS,XREAL_1:9;
 end;
end;
