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

theorem
  c <= a & c <= b & a -' c = b -' c implies a = b
proof
  assume that
A1: a >= c and
A2: b >= c and
A3: a -' c = b -' c;
  a - c >= 0 by A1,Th48;
  then
A4: a -' c = a - c by XREAL_0:def 2;
  b - c >= 0 by A2,Th48;
  then a + (-c) = b + (-c) by A3,A4,XREAL_0:def 2;
  hence thesis;
end;
