36 lines
643 B
Coq
36 lines
643 B
Coq
(* week-05_eqn-and-remember.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 16 Feb 2024 *)
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(* ********** *)
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Lemma O_or_S :
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forall n : nat,
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n = 0 \/ exists n' : nat, n = S n'.
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Proof.
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intro n.
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case n as [ | n'] eqn:H_n.
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- left.
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reflexivity.
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- right.
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exists n'.
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reflexivity.
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Qed.
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(* ********** *)
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Lemma add_1_r :
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forall n : nat,
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n + 1 = S n.
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Proof.
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intro n.
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remember (n + 1) as n_plus_1 eqn:H_n_plus_1.
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remember (S n) as Sn eqn:H_Sn.
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remember (n_plus_1 = Sn) as prove_me eqn:goal.
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Abort.
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(* ********** *)
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(* end of week-05_eqn-and-remember.v *)
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