reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem
  b <> 0 & c <> 0 implies (r*b+c) / b > r
  proof
    assume that
A1: b <> 0 and
A2: c <> 0;
A3: (r*b+c) / b = r*b/b + c/b
    .= r + c/b by A1,XCMPLX_1:89;
    r + c/b > r + 0 by A1,A2,XREAL_1:8;
    hence thesis by A3;
  end;
