--
--  Copyright (C) 2016-2025, AdaCore
--
--  SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
--

package body SPARK.Lemmas.Mod_Arithmetic
  with SPARK_Mode => Off --  #BODYMODE
is

   procedure Lemma_Div_Is_Monotonic (Val1 : Uint; Val2 : Uint; Denom : Pos)
   is null;

   procedure Lemma_Div_Then_Mult_Bounds (Arg1 : Uint; Arg2 : Pos; Res : Uint)
   is
   begin
      pragma Assert (Res <= Arg1);
      pragma Assert (Arg1 - Res < Arg2);
   end Lemma_Div_Then_Mult_Bounds;

   procedure Lemma_Mult_Is_Monotonic (Val1 : Uint; Val2 : Uint; Factor : Uint)
   is null;

   procedure Lemma_Mult_Is_Strictly_Monotonic
     (Val1 : Uint; Val2 : Uint; Factor : Pos)
   is null;

   procedure Lemma_Mult_Protect (Arg1 : Uint; Arg2 : Uint; Upper_Bound : Uint)
   is null;

   procedure Lemma_Mult_Scale
     (Val : Uint; Scale_Num : Uint; Scale_Denom : Pos; Res : Uint)
   is null;

   procedure Lemma_Mult_Then_Div_Is_Ident (Arg1 : Uint; Arg2 : Pos) is null;

   procedure Lemma_Mult_Then_Mod_Is_Zero (Arg1 : Uint; Arg2 : Pos) is null;

end SPARK.Lemmas.Mod_Arithmetic;
