Formal Verification of Hardware Components in Critical Systems

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Example of interactive formal proof in Coq.

(1)	Inductive Nat : Type :=
(2)	|O : Nat
(3)	|Succ : Nat ⟶ Nat.
(4)	Fixpoint Add (n m: Nat) : Nat :=
(5)	match n with
(6)	|O ⟹ m
(7)	|Succ ⟹ S (Add m)
(8)	end.
(9)	Lemma Add_N_O: n:Nat, Add n O = n.
(10)	Proof.
(11)	induction n.
(12)	(CASE 1: n is O)
(13)	reflexivity.
(14)	(CASE 2: n is (S n))
(15)	simpl. rewrite IHn. auto.
(16)	Qed.