reserve a,b,c,d for Real;
reserve r,s for Real;
reserve p,q,r,s,t for ExtReal;

theorem
  a <= b & c < a implies b -' a < b -' c
proof
  assume that
A1: a <= b and
A2: c < a;
A3: b - a < b - c by A2,Th15;
  b -' c = b - c by A1,A2,Th233,XXREAL_0:2;
  hence thesis by A1,A3,Th48,XREAL_0:def 2;
end;
