feat: 3234 week 2

cs3234/labs/week-02_the-revert-tactic.v

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