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 = c-b;
  assume c < b;
  then
A2: 0 > c-b by Lm23;
  then (-d)/2 < -d by Lm27;
  then c+-d/2 < c+-d by Lm10;
  then c-d/2 < c-d;
  then c < b+d/2 by Lm16;
  hence contradiction by A1,A2;
end;
