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Definition le_trans := 0.
Module Test_Read.
Module M.
Require Le. (* Reading without importing *)
Check Le.le_trans.
Lemma th0 : le_trans = 0.
reflexivity.
Qed.
End M.
Check Le.le_trans.
Lemma th0 : le_trans = 0.
reflexivity.
Qed.
Import M.
Lemma th1 : le_trans = 0.
reflexivity.
Qed.
End Test_Read.
(****************************************************************)
Definition le_decide := 1. (* from Arith/Compare *)
Definition min := 0. (* from Arith/Min *)
Module Test_Require.
Module M.
Require Import Compare. (* Imports Min as well *)
Lemma th1 : le_decide = le_decide.
reflexivity.
Qed.
Lemma th2 : min = min.
reflexivity.
Qed.
End M.
(* Checks that Compare and List are loaded *)
Check Compare.le_decide.
Check Min.min.
(* Checks that Compare and List are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : min = 0.
reflexivity.
Qed.
(* It should still be the case after Import M *)
Import M.
Lemma th3 : le_decide = 1.
reflexivity.
Qed.
Lemma th4 : min = 0.
reflexivity.
Qed.
End Test_Require.
(****************************************************************)
Module Test_Import.
Module M.
Import Compare. (* Imports Min as well *)
Lemma th1 : le_decide = le_decide.
reflexivity.
Qed.
Lemma th2 : min = min.
reflexivity.
Qed.
End M.
(* Checks that Compare and List are loaded *)
Check Compare.le_decide.
Check Min.min.
(* Checks that Compare and List are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : min = 0.
reflexivity.
Qed.
(* It should still be the case after Import M *)
Import M.
Lemma th3 : le_decide = 1.
reflexivity.
Qed.
Lemma th4 : min = 0.
reflexivity.
Qed.
End Test_Import.
(************************************************************************)
Module Test_Export.
Module M.
Export Compare. (* Exports Min as well *)
Lemma th1 : le_decide = le_decide.
reflexivity.
Qed.
Lemma th2 : min = min.
reflexivity.
Qed.
End M.
(* Checks that Compare and List are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : min = 0.
reflexivity.
Qed.
(* After Import M they should be imported as well *)
Import M.
Lemma th3 : le_decide = le_decide.
reflexivity.
Qed.
Lemma th4 : min = min.
reflexivity.
Qed.
End Test_Export.
(************************************************************************)
Module Test_Require_Export.
Definition mult_sym := 1. (* from Arith/Mult *)
Definition plus_sym := 0. (* from Arith/Plus *)
Module M.
Require Export Mult. (* Exports Plus as well *)
Lemma th1 : mult_comm = mult_comm.
reflexivity.
Qed.
Lemma th2 : plus_comm = plus_comm.
reflexivity.
Qed.
End M.
(* Checks that Mult and Plus are _not_ imported *)
Lemma th1 : mult_sym = 1.
reflexivity.
Qed.
Lemma th2 : plus_sym = 0.
reflexivity.
Qed.
(* After Import M they should be imported as well *)
Import M.
Lemma th3 : mult_comm = mult_comm.
reflexivity.
Qed.
Lemma th4 : plus_comm = plus_comm.
reflexivity.
Qed.
End Test_Require_Export.
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