27 lines
499 B
Coq
27 lines
499 B
Coq
From Coq Require Import Arith List.
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From Coq Require Import Lia.
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Require Import Ring.
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Theorem plus_id_exercise : forall n m o : nat,
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n = m -> m = o -> n + m = m + o.
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Proof.
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lia.
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Qed.
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Theorem add_assoc : forall n m p : nat,
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n + (m + p) = (n + m) + p.
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Proof.
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lia.
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Qed.
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Theorem S_injective : forall (n m : nat),
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S n = S m -> n = m.
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Proof.
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congruence.
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Qed.
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Theorem or_distributes_over_and : forall P Q R : Prop,
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P \/ (Q /\ R) <-> (P \/ Q) /\ (P \/ R).
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Proof.
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intuition.
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Qed.
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