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Yiyun Liu 2025-03-10 15:35:43 -04:00
parent 849d19708e
commit 4cbd2ac0fd
2 changed files with 22 additions and 12 deletions
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16
theories/algorithmic.v
View file

@ -737,8 +737,6 @@ Lemma A_Conf' a b :
algo_dom_r a b. algo_dom_r a b.
Proof. Proof.
move => ha hb. move => ha hb.
have {}ha : HRed.nf a by sfirstorder use:hf_no_hred, hne_no_hred.
have {}hb : HRed.nf b by sfirstorder use:hf_no_hred, hne_no_hred.
move => ?. move => ?.
apply A_NfNf. apply A_NfNf.
by apply A_Conf. by apply A_Conf.
@ -1234,6 +1232,11 @@ Qed.
Lemma algo_dom_r_algo_dom : forall a b, HRed.nf a -> HRed.nf b -> algo_dom_r a b -> algo_dom a b. Lemma algo_dom_r_algo_dom : forall a b, HRed.nf a -> HRed.nf b -> algo_dom_r a b -> algo_dom a b.
Proof. hauto l:on use:algo_dom_r_inv, hreds_nf_refl. Qed. Proof. hauto l:on use:algo_dom_r_inv, hreds_nf_refl. Qed.
Lemma algo_dom_algo_dom_neu : forall a b, ishne a -> ishne b -> algo_dom a b -> algo_dom_neu a b \/ tm_conf a b.
Proof.
inversion 3; subst => //=; tauto.
Qed.
Lemma term_metric_algo_dom : forall k a b, term_metric k a b -> algo_dom_r a b. Lemma term_metric_algo_dom : forall k a b, term_metric k a b -> algo_dom_r a b.
Proof. Proof.
move => [:hneL]. move => [:hneL].
@ -1268,9 +1271,12 @@ Proof.
case : b hfa hfb h => //=; case a => //=; eauto 5 using A_Conf' with adom. case : b hfa hfb h => //=; case a => //=; eauto 5 using A_Conf' with adom.
+ move => a0 b0 a1 b1 nfa0 nfa1. + move => a0 b0 a1 b1 nfa0 nfa1.
move /term_metric_app /(_ nfa0 nfa1) => [j][hj][ha]hb. move /term_metric_app /(_ nfa0 nfa1) => [j][hj][ha]hb.
apply A_NfNf. apply A_AppCong => //; eauto. apply A_NfNf.
have {}nfa0 : HRed.nf a0 by sfirstorder use:hne_no_hred. (* apply A_NfNf. apply A_NeuNeu. apply A_AppCong => //; eauto. *)
have {}nfb0 : HRed.nf a1 by sfirstorder use:hne_no_hred. have nfa0' : HRed.nf a0 by sfirstorder use:hne_no_hred.
have nfb0' : HRed.nf a1 by sfirstorder use:hne_no_hred.
have ha0 : algo_dom a0 a1 by eauto using algo_dom_r_algo_dom.
apply A_Conf. admit. admit. rewrite /tm_conf. simpl.
eauto using algo_dom_r_algo_dom. eauto using algo_dom_r_algo_dom.
+ move => p0 A0 p1 A1 neA0 neA1. + move => p0 A0 p1 A1 neA0 neA1.
have {}nfa0 : HRed.nf A0 by sfirstorder use:hne_no_hred. have {}nfa0 : HRed.nf A0 by sfirstorder use:hne_no_hred.

18
theories/common.v
View file

@ -129,9 +129,9 @@ Definition tm_nonconf (a b : PTm) : bool :=
| _, PPair _ _ => ~~ ishf a | _, PPair _ _ => ~~ ishf a
| PZero, PZero => true | PZero, PZero => true
| PSuc _, PSuc _ => true | PSuc _, PSuc _ => true
| PApp _ _, PApp _ _ => (~~ ishf a) && (~~ ishf b) | PApp _ _, PApp _ _ => true
| PProj _ _, PProj _ _ => (~~ ishf a) && (~~ ishf b) | PProj _ _, PProj _ _ => true
| PInd _ _ _ _, PInd _ _ _ _ => (~~ ishf a) && (~~ ishf b) | PInd _ _ _ _, PInd _ _ _ _ => true
| PNat, PNat => true | PNat, PNat => true
| PUniv _, PUniv _ => true | PUniv _, PUniv _ => true
| PBind _ _ _, PBind _ _ _ => true | PBind _ _ _, PBind _ _ _ => true
@ -140,8 +140,6 @@ Definition tm_nonconf (a b : PTm) : bool :=
Definition tm_conf (a b : PTm) := ~~ tm_nonconf a b. Definition tm_conf (a b : PTm) := ~~ tm_nonconf a b.
Definition ishf_ren (a : PTm) (ξ : nat -> nat) : Definition ishf_ren (a : PTm) (ξ : nat -> nat) :
ishf (ren_PTm ξ a) = ishf a. ishf (ren_PTm ξ a) = ishf a.
Proof. case : a => //=. Qed. Proof. case : a => //=. Qed.
@ -262,8 +260,8 @@ Inductive algo_dom : PTm -> PTm -> Prop :=
algo_dom a b algo_dom a b
| A_Conf a b : | A_Conf a b :
HRed.nf a -> ishf a ->
HRed.nf b -> ishf b ->
tm_conf a b -> tm_conf a b ->
algo_dom a b algo_dom a b
@ -296,6 +294,12 @@ with algo_dom_neu : PTm -> PTm -> Prop :=
algo_dom_r c0 c1 -> algo_dom_r c0 c1 ->
algo_dom_neu (PInd P0 u0 b0 c0) (PInd P1 u1 b1 c1) algo_dom_neu (PInd P0 u0 b0 c0) (PInd P1 u1 b1 c1)
| A_NeuConf a b :
ishne a ->
ishne b ->
tm_conf a b ->
algo_dom_neu a b
with algo_dom_r : PTm -> PTm -> Prop := with algo_dom_r : PTm -> PTm -> Prop :=
| A_NfNf a b : | A_NfNf a b :
algo_dom a b -> algo_dom a b ->