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Add check_equal_conf case

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Yiyun Liu 2025-03-04 23:22:41 -05:00
parent c05bd10016
commit c1ff0ae145
1 changed files with 32 additions and 19 deletions
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49
theories/executable.v
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@ -3,22 +3,26 @@ Require Import Autosubst2.core Autosubst2.unscoped Autosubst2.syntax common.
Require Import Logic.PropExtensionality (propositional_extensionality).
Require Import ssreflect ssrbool.
Import Logic (inspect).
From Ltac2 Require Import Ltac2.
Import Ltac2.Constr.
Set Default Proof Mode "Classic".
Require Import ssreflect ssrbool.
From Hammer Require Import Tactics.
Definition tm_nonconf (a b : PTm) : bool :=
match a, b with
| PAbs _, _ => ishne b || isabs b
| _, PAbs _ => ishne a
| PAbs _, _ => (~~ ishf b) || isabs b
| _, PAbs _ => ~~ ishf a
| VarPTm _, VarPTm _ => true
| PPair _ _, _ => ishne b || ispair b
| _, PPair _ _ => ishne a
| PPair _ _, _ => (~~ ishf b) || ispair b
| _, PPair _ _ => ~~ ishf a
| PZero, PZero => true
| PSuc _, PSuc _ => true
| PApp _ _, PApp _ _ => ishne a && ishne b
| PProj _ _, PProj _ _ => ishne a && ishne b
| PInd _ _ _ _, PInd _ _ _ _ => ishne a && ishne b
| PApp _ _, PApp _ _ => (~~ ishf a) && (~~ ishf b)
| PProj _ _, PProj _ _ => (~~ ishf a) && (~~ ishf b)
| PInd _ _ _ _, PInd _ _ _ _ => (~~ ishf a) && (~~ ishf b)
| PNat, PNat => true
| PUniv _, PUniv _ => true
| PBind _ _ _, PBind _ _ _ => true
@ -184,9 +188,11 @@ Inductive algo_dom : PTm -> PTm -> Prop :=
algo_dom_r c0 c1 ->
algo_dom (PInd P0 u0 b0 c0) (PInd P1 u1 b1 c1)
(* | A_Conf a b : *)
(* tm_conf a b -> *)
(* algo_dom a b *)
| A_Conf a b :
HRed.nf a ->
HRed.nf b ->
tm_conf a b ->
algo_dom a b
with algo_dom_r : PTm -> PTm -> Prop :=
| A_NfNf a b :
@ -283,11 +289,19 @@ Definition fancy_hred (a : PTm) : HRed.nf a + {b | HRed.R a b}.
left. move => b /hred_complete. congruence.
Defined.
Ltac2 destruct_algo () :=
lazy_match! goal with
| [h : algo_dom ?a ?b |- _ ] =>
if is_var a then destruct $a; ltac1:(done) else
(if is_var b then destruct $b; ltac1:(done) else ())
end.
Ltac check_equal_triv :=
intros;subst;
lazymatch goal with
(* | [h : algo_dom (VarPTm _) (PAbs _) |- _] => idtac *)
| [h : algo_dom _ _ |- _] => try (inversion h; by subst)
| [h : algo_dom _ _ |- _] => try (inversion h; subst => //=; ltac2:(Control.enter destruct_algo))
| _ => idtac
end.
@ -337,6 +351,7 @@ Ltac solve_check_equal :=
| inr b' := check_equal_r a (proj1_sig b') _;
| inl h'' := check_equal a b _.
Next Obligation.
intros.
inversion h; subst => //=.
@ -363,12 +378,6 @@ Next Obligation.
Defined.
(* Next Obligation. *)
(* qauto inv:algo_dom, algo_dom_r. *)
(* Defined. *)
Lemma check_equal_abs_abs a b h : check_equal (PAbs a) (PAbs b) (A_AbsAbs a b h) = check_equal_r a b h.
Proof. reflexivity. Qed.
@ -468,4 +477,8 @@ Proof.
sfirstorder use:hne_no_hred, hf_no_hred.
Qed.
#[export]Hint Rewrite check_equal_abs_abs check_equal_abs_neu check_equal_neu_abs check_equal_pair_pair check_equal_pair_neu check_equal_neu_pair check_equal_bind_bind check_equal_hredl check_equal_hredr check_equal_nfnf : ce_prop.
Lemma check_equal_conf a b nfa nfb nfab :
check_equal a b (A_Conf a b nfa nfb nfab) = false.
Proof. destruct a; destruct b => //=. Qed.
#[export]Hint Rewrite check_equal_abs_abs check_equal_abs_neu check_equal_neu_abs check_equal_pair_pair check_equal_pair_neu check_equal_neu_pair check_equal_bind_bind check_equal_hredl check_equal_hredr check_equal_nfnf check_equal_conf : ce_prop.