reserve a,b,c,d,e for Real;

theorem Th02:
  b - a <= c & a <= b implies |. b - a .| <= c
  proof
    assume that
A1: b - a <= c and
A2: a <= b;
A3: a - a <= b - a by A2,XREAL_1:9;
    then -c <= 0 by A1;
    hence thesis by A3,A1,ABSVALUE:5;
  end;
