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Definition le_trans := 0.
Module Test_Read.
Module M.
Require PeanoNat. (* Reading without importing *)
Check PeanoNat.Nat.le_trans.
Lemma th0 : le_trans = 0.
reflexivity.
Qed.
End M.
Check PeanoNat.Nat.le_trans.
Lemma th0 : le_trans = 0.
reflexivity.
Qed.
Import M.
Lemma th1 : le_trans = 0.
reflexivity.
Qed.
End Test_Read.
(****************************************************************)
(* Arith.Compare containes Require Export Wf_nat. *)
Definition le_decide := 1. (* from Arith/Compare *)
Definition lt_wf := 0. (* from Arith/Wf_nat *)
Module Test_Require.
Module M.
Require Import Compare. (* Imports Compare_dec as well *)
Lemma th1 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th2 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End M.
(* Checks that Compare and Wf_nat are loaded *)
Check Compare.le_decide.
Check Wf_nat.lt_wf.
(* Checks that Compare and Wf_nat are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : lt_wf = 0.
reflexivity.
Qed.
(* It should still be the case after Import M *)
Import M.
Lemma th3 : le_decide = 1.
reflexivity.
Qed.
Lemma th4 : lt_wf = 0.
reflexivity.
Qed.
End Test_Require.
(****************************************************************)
Module Test_Import.
Module M.
Import Compare. (* Imports Wf_nat as well *)
Lemma th1 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th2 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End M.
(* Checks that Compare and Wf_nat are loaded *)
Check Compare.le_decide.
Check Wf_nat.lt_wf.
(* Checks that Compare and Wf_nat are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : lt_wf = 0.
reflexivity.
Qed.
(* It should still be the case after Import M *)
Import M.
Lemma th3 : le_decide = 1.
reflexivity.
Qed.
Lemma th4 : lt_wf = 0.
reflexivity.
Qed.
End Test_Import.
(************************************************************************)
Module Test_Export.
Module M.
Export Compare. (* Exports Wf_nat as well *)
Lemma th1 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th2 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End M.
(* Checks that Compare and Wf_nat are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : lt_wf = 0.
reflexivity.
Qed.
(* After Import M they should be imported as well *)
Import M.
Lemma th3 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th4 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End Test_Export.
(************************************************************************)
Module Test_Require_Export.
Definition le_decide := 1. (* from Arith/Compare *)
Definition lt_wf := 0. (* from Arith/Wf_nat *)
Module M.
Require Export Compare. (* Exports Wf_nat as well *)
Lemma th1 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th2 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End M.
(* Checks that Compare and Wf_nat are _not_ imported *)
Lemma th1 : le_decide = 1.
reflexivity.
Qed.
Lemma th2 : lt_wf = 0.
reflexivity.
Qed.
(* After Import M they should be imported as well *)
Import M.
Lemma th3 n : le_decide n = le_decide n.
reflexivity.
Qed.
Lemma th4 n : lt_wf n = lt_wf n.
reflexivity.
Qed.
End Test_Require_Export.
|
