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Add back preservation lemma for ered
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Needed for justifying that the extended algorithm
This commit is contained in:
Yiyun Liu 2025-05-20 14:41:09 -04:00
parent 4c527c1b81
commit d2576f21fc
1 changed files with 14 additions and 1 deletions
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15
theories/fp_red.v
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@ -719,6 +719,8 @@ Module RRed.
move => */=; apply : IndSuc'; eauto. by asimpl. move => */=; apply : IndSuc'; eauto. by asimpl.
Qed. Qed.
Lemma abs_preservation a b : isabs a -> R a b -> isabs b. hauto q:on inv:R. Qed.
End RRed. End RRed.
Module RPar. Module RPar.
@ -1004,6 +1006,9 @@ Qed.
Module RReds. Module RReds.
Lemma abs_preservation a b : isabs a -> rtc RRed.R a b -> isabs b.
induction 2; hauto lq:on use:RRed.abs_preservation. Qed.
#[local]Ltac solve_s_rec := #[local]Ltac solve_s_rec :=
move => *; eapply rtc_l; eauto; move => *; eapply rtc_l; eauto;
hauto lq:on ctrs:RRed.R. hauto lq:on ctrs:RRed.R.
@ -1755,6 +1760,15 @@ Module ERed.
Derive Inversion inv with (forall (a b : PTm), R a b) Sort Prop. Derive Inversion inv with (forall (a b : PTm), R a b) Sort Prop.
Lemma abs_back_preservation (a b : PTm) :
SN a -> R a b -> isabs b -> isabs a.
Proof.
move => + h.
elim : a b /h => //=.
case => //=. move => p. move /SN_NoForbid.P_PairInv.
sfirstorder use:SN_NoForbid.PProj_imp.
Qed.
Lemma ToEPar (a b : PTm) : Lemma ToEPar (a b : PTm) :
ERed.R a b -> EPar.R a b. ERed.R a b -> EPar.R a b.
Proof. Proof.
@ -3292,7 +3306,6 @@ Module DJoin.
Qed. Qed.
End DJoin. End DJoin.
Module Sub1. Module Sub1.
Inductive R : PTm -> PTm -> Prop := Inductive R : PTm -> PTm -> Prop :=
| Refl a : | Refl a :