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30 lines
571 B
Coq
30 lines
571 B
Coq
Require Import Relations.
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Set Implicit Arguments.
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Section Invariant.
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Variable state : Type.
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Variable step : state -> state -> Prop.
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Variable invariant : state -> Prop.
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Hint Constructors trc.
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Definition safe (s : state) :=
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forall s', step^* s s' -> invariant s'.
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Variable s0 : state.
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Hypothesis Hinitial : invariant s0.
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Hypothesis Hstep : forall s s', invariant s -> step s s' -> invariant s'.
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Lemma safety : safe s0.
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Proof.
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generalize dependent s0.
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unfold safe.
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induction 2; eauto.
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Qed.
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End Invariant.
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Hint Resolve safety.
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