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

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