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Prove that ered is strongly normalizing

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Yiyun Liu 2025-01-31 20:54:33 -05:00
parent f57e10be93
commit 580e3a8251
1 changed files with 33 additions and 2 deletions
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35
theories/fp_red.v
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@ -4,9 +4,9 @@ Import Ltac2.Notations.
Import Ltac2.Control.
Require Import ssreflect ssrbool.
Require Import FunInd.
Require Import Arith.Wf_nat.
Require Import Arith.Wf_nat (well_founded_lt_compat).
Require Import Psatz.
From stdpp Require Import relations (rtc (..), rtc_once, rtc_r).
From stdpp Require Import relations (rtc (..), rtc_once, rtc_r, sn).
From Hammer Require Import Tactics.
Require Import Autosubst2.core Autosubst2.fintype Autosubst2.syntax.
Require Import Btauto.
@ -1438,4 +1438,35 @@ Module LoReds.
have : ~~ ishf a by inversion h.
hauto lq:on ctrs:LoRed.R.
Qed.
End LoReds.
Fixpoint size_PTm {n} (a : PTm n) :=
match a with
| VarPTm _ => 1
| PAbs a => 1 + size_PTm a
| PApp a b => 1 + Nat.add (size_PTm a) (size_PTm b)
| PProj p a => 1 + size_PTm a
| PPair a b => 1 + Nat.add (size_PTm a) (size_PTm b)
end.
Lemma size_PTm_ren n m (ξ : fin n -> fin m) a : size_PTm (ren_PTm ξ a) = size_PTm a.
Proof.
move : m ξ. elim : n / a => //=; scongruence.
Qed.
#[export]Hint Rewrite size_PTm_ren : sizetm.
Lemma ered_size {n} (a b : PTm n) :
ERed.R a b ->
size_PTm b < size_PTm a.
Proof.
move => h. elim : n a b /h; hauto l:on rew:db:sizetm.
Qed.
Lemma ered_sn n (a : PTm n) : sn ERed.R a.
Proof.
hauto lq:on rew:off use:size_PTm_ren, ered_size,
well_founded_lt_compat unfold:well_founded.
Qed.