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Progress on porting to Coq 8.6
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Adam Chlipala
parent
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commit
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5 changed files with 146 additions and 42 deletions
78
Frap.v
78
Frap.v
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@ -19,7 +19,79 @@ Ltac inductN n :=
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end
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end.
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Ltac induct e := inductN e || dependent induction e.
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Ltac same_structure x y :=
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match x with
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| ?f ?a1 ?b1 ?c1 ?d1 =>
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match y with
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| f ?a2 ?b2 ?c2 ?d2 => same_structure a1 a2; same_structure b1 b2; same_structure c1 c2; same_structure d1 d2
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| _ => fail 2
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end
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| ?f ?a1 ?b1 ?c1 =>
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match y with
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| f ?a2 ?b2 ?c2 => same_structure a1 a2; same_structure b1 b2; same_structure c1 c2
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| _ => fail 2
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end
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| ?f ?a1 ?b1 =>
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match y with
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| f ?a2 ?b2 => same_structure a1 a2; same_structure b1 b2
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| _ => fail 2
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end
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| ?f ?a1 =>
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match y with
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| f ?a2 => same_structure a1 a2
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| _ => fail 2
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end
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| _ =>
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match y with
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| ?f ?a1 ?b1 ?c1 ?d1 =>
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match x with
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| f ?a2 ?b2 ?c2 ?d2 => same_structure a1 a2; same_structure b1 b2; same_structure c1 c2; same_structure d1 d2
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| _ => fail 2
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end
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| ?f ?a1 ?b1 ?c1 =>
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match x with
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| f ?a2 ?b2 ?c2 => same_structure a1 a2; same_structure b1 b2; same_structure c1 c2
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| _ => fail 2
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end
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| ?f ?a1 ?b1 =>
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match x with
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| f ?a2 ?b2 => same_structure a1 a2; same_structure b1 b2
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| _ => fail 2
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end
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| ?f ?a1 =>
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match x with
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| f ?a2 => same_structure a1 a2
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| _ => fail 2
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end
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| _ => idtac
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end
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end.
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Ltac instantiate_obvious1 H :=
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match type of H with
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| ?x = ?y -> _ =>
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(same_structure x y; specialize (H eq_refl)) || fail 3
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| JMeq.JMeq ?x ?y -> _ =>
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(same_structure x y; specialize (H JMeq.JMeq_refl)) || fail 3
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| forall x : ?T, _ =>
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match type of T with
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| Prop => fail 1
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| _ =>
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let x' := fresh x in
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evar (x' : T);
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let x'' := eval unfold x' in x' in specialize (H x''); clear x';
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instantiate_obvious1 H
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end
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end.
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Ltac instantiate_obvious H := repeat instantiate_obvious1 H.
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Ltac instantiate_obviouses :=
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repeat match goal with
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| [ H : _ |- _ ] => instantiate_obvious H
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end.
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Ltac induct e := (inductN e || dependent induction e); instantiate_obviouses.
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Ltac invert' H := inversion H; clear H; subst.
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@ -244,9 +316,9 @@ Ltac total_ordering N M := destruct (totally_ordered N M).
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Ltac inList x xs :=
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match xs with
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| (x, _) => constr:true
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| (x, _) => true
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| (_, ?xs') => inList x xs'
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| _ => constr:false
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| _ => false
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end.
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Ltac maybe_simplify_map m found kont :=
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@ -630,25 +630,26 @@ Module Stlc.
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propositional.
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right.
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invert H1; invert H.
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invert H2; invert H0.
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(* Some automation is needed here to maintain compatibility with
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* name generation in different Coq versions. *)
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match goal with
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| [ H1 : value e1, H2 : hasty $0 e1 _ |- _ ] => invert H1; invert H2
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end.
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match goal with
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| [ H1 : value e2, H2 : hasty $0 e2 _ |- _ ] => invert H1; invert H2
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end.
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exists (Const (n + n0)).
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eapply StepRule with (C := Hole).
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eauto.
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eauto.
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constructor.
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invert H2.
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right.
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invert H3.
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exists (Plus e1 x).
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eapply StepRule with (C := Plus2 e1 C).
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eauto.
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eauto.
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assumption.
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invert H1.
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invert H3.
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match goal with
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| [ H : exists x, _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (Plus x e2).
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eapply StepRule with (C := Plus1 C e2).
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@ -656,8 +657,25 @@ Module Stlc.
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eauto.
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assumption.
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invert H1.
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invert H3.
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match goal with
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| [ H : exists x, _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (Plus e1 x).
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eapply StepRule with (C := Plus2 e1 C).
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eauto.
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eauto.
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assumption.
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match goal with
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| [ H : exists x, step e1 _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (Plus x e2).
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eapply StepRule with (C := Plus1 C e2).
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@ -671,7 +689,9 @@ Module Stlc.
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propositional.
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right.
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invert H1; invert H.
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match goal with
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| [ H1 : value e1, H2 : hasty $0 e1 _ |- _ ] => invert H1; invert H2
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end.
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exists (subst e2 x e0).
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eapply StepRule with (C := Hole).
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eauto.
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@ -679,17 +699,12 @@ Module Stlc.
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constructor.
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assumption.
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invert H2.
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right.
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invert H3.
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exists (App e1 x).
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eapply StepRule with (C := App2 e1 C).
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eauto.
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eauto.
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assumption.
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invert H1.
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invert H3.
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match goal with
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| [ H : exists x, _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (App x e2).
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eapply StepRule with (C := App1 C e2).
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@ -697,8 +712,25 @@ Module Stlc.
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eauto.
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assumption.
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invert H1.
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invert H3.
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match goal with
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| [ H : exists x, _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (App e1 x).
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eapply StepRule with (C := App2 e1 C).
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eauto.
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eauto.
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assumption.
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match goal with
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| [ H : exists x, step e1 _ |- _ ] => invert H
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end.
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match goal with
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| [ H : step _ _ |- _ ] => invert H
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end.
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right.
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exists (App x e2).
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eapply StepRule with (C := App1 C e2).
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@ -775,10 +807,8 @@ Module Stlc.
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constructor.
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constructor.
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apply IHhasty1.
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assumption.
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apply IHhasty2.
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assumption.
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eapply IHhasty1; equality.
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eapply IHhasty2; equality.
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cases (x0 ==v x).
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@ -800,10 +830,8 @@ Module Stlc.
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assumption.
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econstructor.
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apply IHhasty1.
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assumption.
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apply IHhasty2.
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assumption.
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eapply IHhasty1; equality.
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eapply IHhasty2; equality.
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Qed.
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(* We're almost ready for the other main property. Let's prove it first
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@ -813,6 +813,8 @@ Module Concurrent.
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-> cstep (v, c) (v', c').
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Proof.
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induct 1; repeat match goal with
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| [ H : forall a b c d, _ = _ -> _ = _ -> _ |- _ ] =>
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specialize (H _ _ _ _ eq_refl eq_refl)
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| [ H : cstep _ _ |- _ ] => invert H
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end; eauto.
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Qed.
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@ -854,7 +854,8 @@ Proof.
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cases (x0 $? a); try equality.
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eauto using lookup_Some_dom.
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eauto using lookup_Some_dom.
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rewrite lookup_join2 in H8; eauto.
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rewrite lookup_join2 in H8.
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eapply H2; eassumption.
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eauto using lookup_None_dom.
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Qed.
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@ -1102,7 +1102,8 @@ Proof.
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cases (x0 $? a); try equality.
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eauto using lookup_Some_dom.
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eauto using lookup_Some_dom.
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rewrite lookup_join2 in H8; eauto.
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rewrite lookup_join2 in H8.
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eapply H2; eassumption.
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eauto using lookup_None_dom.
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Qed.
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