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 b >= c
proof
  assume
A1: for a st a < 0 holds b-a >= c;
  set d = b-c;
  assume b < c;
  then
A2: 0 > b-c by Lm23;
  then (-d)/2 < -d by Lm27;
  then b+-d/2 < b+-d by Lm10;
  then b-d/2 < b-d;
  hence contradiction by A1,A2;
end;
