--
--  Copyright (C) 2017-2025, AdaCore
--
--  SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
--

package body SPARK.Lemmas.Floating_Point_Arithmetic
  with SPARK_Mode => Off --  #BODYMODE
is
   procedure Lemma_Add_Is_Monotonic (Val1 : Fl; Val2 : Fl; Val3 : Fl) is null;

   procedure Lemma_Div_Is_Monotonic (Val1 : Fl; Val2 : Fl; Val3 : Fl) is null;

   procedure Lemma_Div_Left_Is_Monotonic (Val1 : Fl; Val2 : Fl; Val3 : Fl)
   is null;

   procedure Lemma_Div_Right_Negative_Is_Monotonic
     (Val1 : Fl; Val2 : Fl; Val3 : Fl)
   is null;

   procedure Lemma_Integer_Add_Exact
     (Val1 : Fl; Val2 : Fl; Int1 : Int; Int2 : Int)
   is null;

   procedure Lemma_Integer_Mul_Exact
     (Val1 : Fl; Val2 : Fl; Int1 : Int; Int2 : Int)
   is null;

   procedure Lemma_Integer_Sub_Exact
     (Val1 : Fl; Val2 : Fl; Int1 : Int; Int2 : Int)
   is null;

   procedure Lemma_Mult_Is_Monotonic (Val1 : Fl; Val2 : Fl; Val3 : Fl) is null;

   procedure Lemma_Mult_By_Less_Than_One (Val1 : Fl; Val2 : Fl) is null;

   procedure Lemma_Mult_Right_Negative_Is_Monotonic
     (Val1 : Fl; Val2 : Fl; Val3 : Fl)
   is null;

   procedure Lemma_Rounding_Error_Add (Val1 : Fl; Val2 : Fl) is null;

   procedure Lemma_Rounding_Error_Div (Val1 : Fl; Val2 : Fl) is null;

   procedure Lemma_Rounding_Error_Mul (Val1 : Fl; Val2 : Fl) is null;

   procedure Lemma_Rounding_Error_Sub (Val1 : Fl; Val2 : Fl) is null;

   procedure Lemma_Sub_Is_Monotonic (Val1 : Fl; Val2 : Fl; Val3 : Fl) is null;

end SPARK.Lemmas.Floating_Point_Arithmetic;
