reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  (for a being Real st a > 0 holds b-a <= c) implies b <= c
proof
  assume
A1: for a st a > 0 holds b-a <= c;
  set d = b-c;
  assume b > c;
  then
A2: 0 < d by Lm21;
  then c+d/2 < c+d by Lm10,Lm27;
  then c < b-d/2 by Lm19;
  hence contradiction by A1,A2;
end;
