reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem
  for a,b being Real holds 0 <= a & a < b implies |.a.| < |.b.|
  proof
    let a,b be Real;
    assume
A1: 0 <= a;
    then |.a.| = a by ABSVALUE:def 1;
    hence thesis by A1,ABSVALUE:def 1;
  end;
