reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;

theorem Th11:
  for f being constant Function of REAL,REAL holds
  f`| = REAL --> 0
  proof
    let f be constant Function of REAL,REAL;
    reconsider z = 0 as Element of REAL by XREAL_0:def 1;
    f`| = REAL --> z
    proof
      let r be Element of REAL;
A1:   f|REAL = f;
      dom f = REAL by FUNCT_2:def 1;
      hence f`|.r = z by A1,Lm1,FDIFF_1:22
      .= (REAL --> z).r;
    end;
    hence thesis;
  end;
