------------------------------------------------------------------------------
--                                                                          --
--                        SPARK LIBRARY COMPONENTS                          --
--                                                                          --
--                        S P A R K . L E M M A S .                         --
--               F I X E D _ P O I N T _ A R I T H M E T I C                --
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--                                 B o d y                                  --
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--                     Copyright (C) 2018-2023, AdaCore                     --
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-- SPARK is free software;  you can  redistribute it and/or modify it under --
-- terms of the  GNU General Public License as published  by the Free Soft- --
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-- sion. SPARK is distributed in the hope that it will be useful, but WITH- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- You should have received a copy of the GNU General Public License and    --
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------------------------------------------------------------------------------

package body SPARK.Lemmas.Fixed_Point_Arithmetic is

   procedure GNAT_Lemma_Div_Is_Monotonic
     (Num1  : Fix;
      Num2  : Fix;
      Denom : Positive)
   is null;

   procedure GNAT_Lemma_Div_Right_Is_Monotonic
     (Num    : Fix;
      Denom1 : Positive;
      Denom2 : Positive)
   is null;

   procedure GNAT_Lemma_Mult_Then_Div_Is_Ident
     (Val1 : Fix;
      Val2 : Positive)
   is null;

end SPARK.Lemmas.Fixed_Point_Arithmetic;
