68 lines
1.2 KiB
Coq
68 lines
1.2 KiB
Coq
(* week-02_the-revert-tactic.v *)
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(* LPP 2024 - CS3234 2023-2024, Sem2 *)
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(* Olivier Danvy <danvy@yale-nus.edu.sg> *)
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(* Version of 28 Jan 2024, with an instance of revert with several arguments *)
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(* was: *)
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(* Version of 25 Jan 2024 *)
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(* ********** *)
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Lemma a_proposition_implies_itself :
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forall A : Prop,
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A -> A.
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Proof.
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intro A.
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intro H_A.
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exact H_A.
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Restart.
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intro A.
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intro H_A.
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revert H_A. (* <-- *)
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revert A. (* <-- *)
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intros A H_A.
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exact H_A.
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Qed.
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(* ********** *)
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Lemma swapping_the_order_of_quantifiers :
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forall A B : Prop,
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(A -> B -> A /\ B) -> B -> A -> A /\ B.
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Proof.
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intros A B H_implication H_B H_A.
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exact (H_implication H_A H_B).
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Restart.
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intros A B H_implication H_B H_A.
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revert H_B.
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revert H_A.
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exact H_implication.
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Restart.
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intros A B H_implication H_B H_A.
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revert H_B.
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revert H_A.
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revert H_implication.
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exact (a_proposition_implies_itself (A -> B -> A /\ B)).
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Restart.
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intros A B H_implication H_B H_A.
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revert H_A H_B.
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exact H_implication.
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Restart.
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intros A B H_implication H_B H_A.
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revert H_implication H_A H_B.
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exact (a_proposition_implies_itself (A -> B -> A /\ B)).
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Qed.
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(* ********** *)
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(* end of week-02_the-revert-tactic.v *)
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