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Some tactic tweaks in preparation for Lab 3
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19
Frap.v
19
Frap.v
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@ -124,7 +124,7 @@ Ltac model_check_step :=
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Ltac model_check_steps1 := model_check_done || model_check_step.
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Ltac model_check_steps := repeat model_check_steps1.
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Ltac model_check_finish := simplify; propositional; subst; simplify; equality.
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Ltac model_check_finish := simplify; propositional; subst; simplify; try equality; try linear_arithmetic.
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Ltac model_check_infer :=
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apply multiStepClosure_ok; simplify; model_check_steps.
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@ -133,3 +133,20 @@ Ltac model_check_find_invariant :=
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simplify; eapply invariant_weaken; [ model_check_infer | ]; cbv beta in *.
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Ltac model_check := model_check_find_invariant; model_check_finish.
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Inductive ordering (n m : nat) :=
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| Lt (_ : n < m)
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| Eq (_ : n = m)
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| Gt (_ : n > m).
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Local Hint Constructors ordering.
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Local Hint Extern 1 (_ < _) => omega.
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Local Hint Extern 1 (_ > _) => omega.
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Theorem totally_ordered : forall n m, ordering n m.
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Proof.
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induction n; destruct m; simpl; eauto.
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destruct (IHn m); eauto.
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Qed.
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Ltac total_ordering N M := destruct (totally_ordered N M).
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