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Fix name change errors for EPar

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Yiyun Liu 2025-01-31 17:32:35 -05:00
parent 5dd3428e2b
commit 571779a4dd
1 changed files with 19 additions and 19 deletions
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38
theories/fp_red.v
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@ -888,7 +888,7 @@ Module NeEPar.
Lemma ToEPar : forall n, (forall (a b : PTm n), R_elim a b -> EPar.R a b) /\
(forall (a b : PTm n), R_nonelim a b -> EPar.R a b).
Proof.
apply ered_mutual; qauto l:on ctrs:EPar.R.
apply epar_mutual; qauto l:on ctrs:EPar.R.
Qed.
End NeEPar.
@ -1092,9 +1092,9 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
Lemma eta_postponement n a b c :
@P n a ->
ERed.R a b ->
EPar.R a b ->
RRed.R b c ->
exists d, rtc RRed.R a d /\ ERed.R d c.
exists d, rtc RRed.R a d /\ EPar.R d c.
Proof.
move => + h.
move : c.
@ -1104,17 +1104,17 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
move => [d [h0 h1]].
exists (PAbs (PApp (ren_PTm shift d) (VarPTm var_zero))).
split. hauto lq:on rew:off ctrs:rtc use:RReds.AbsCong, RReds.AppCong, RReds.renaming.
hauto lq:on ctrs:ERed.R.
hauto lq:on ctrs:EPar.R.
- move => n a0 a1 ha iha c /P_PairInv [/P_ProjInv + _].
move /iha => /[apply].
move => [d [h0 h1]].
exists (PPair (PProj PL d) (PProj PR d)).
hauto lq:on ctrs:ERed.R use:RReds.PairCong, RReds.ProjCong.
hauto lq:on ctrs:EPar.R use:RReds.PairCong, RReds.ProjCong.
- move => n a0 a1 ha iha c /P_AbsInv /[swap].
elim /RRed.inv => //=_.
move => a2 a3 + [? ?]. subst.
move : iha; repeat move/[apply].
hauto lq:on use:RReds.AbsCong ctrs:ERed.R.
hauto lq:on use:RReds.AbsCong ctrs:EPar.R.
- move => n a0 a1 b0 b1 ha iha hb ihb c hP.
elim /RRed.inv => //= _.
+ move => a2 b2 [*]. subst.
@ -1125,7 +1125,7 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
inversion h1; subst.
* inversion H0; subst.
exists (subst_PTm (scons b0 VarPTm) a3).
split; last by scongruence use:ERed.morphing.
split; last by scongruence use:EPar.morphing.
apply : relations.rtc_transitive.
apply RReds.AppCong.
eassumption.
@ -1145,22 +1145,22 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
split.
apply : rtc_r; last by apply RRed.AppAbs.
hauto lq:on ctrs:rtc use:RReds.AppCong.
hauto l:on inv:option use:ERed.morphing,NeERed.ToERed.
hauto l:on inv:option use:EPar.morphing,NeEPar.ToEPar.
+ move => a2 a3 b2 ha2 [*]. subst.
move : iha (ha2) {ihb} => /[apply].
have : P a0 by sfirstorder use:P_AppInv.
move /[swap]/[apply].
move => [d [h0 h1]].
exists (PApp d b0).
hauto lq:on ctrs:ERed.R, rtc use:RReds.AppCong.
hauto lq:on ctrs:EPar.R, rtc use:RReds.AppCong.
+ move => a2 b2 b3 hb2 [*]. subst.
move {iha}.
have : P b0 by sfirstorder use:P_AppInv.
move : ihb hb2; repeat move /[apply].
hauto lq:on rew:off ctrs:ERed.R, rtc use:RReds.AppCong.
hauto lq:on rew:off ctrs:EPar.R, rtc use:RReds.AppCong.
- move => n a0 a1 b0 b1 ha iha hb ihb c /P_PairInv [hP hP'].
elim /RRed.inv => //=_;
hauto lq:on rew:off ctrs:ERed.R, rtc use:RReds.PairCong.
hauto lq:on rew:off ctrs:EPar.R, rtc use:RReds.PairCong.
- move => n p a0 a1 ha iha c /[dup] hP /P_ProjInv hP'.
elim / RRed.inv => //= _.
+ move => p0 a2 b0 [*]. subst.
@ -1170,7 +1170,7 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
* qauto l:on ctrs:rtc use:RReds.ProjCong, P_ProjAbs, P_RReds.
* inversion H0; subst.
exists (if p is PL then a1 else b1).
split; last by scongruence use:NeERed.ToERed.
split; last by scongruence use:NeEPar.ToEPar.
apply : relations.rtc_transitive.
apply RReds.ProjCong; eauto.
apply : rtc_l.
@ -1183,22 +1183,22 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
apply RRed.ProjPair.
apply rtc_once. apply RRed.ProjPair.
* exists (if p is PL then a3 else b1).
split; last by hauto lq:on use:NeERed.ToERed.
split; last by hauto lq:on use:NeEPar.ToEPar.
apply : relations.rtc_transitive.
eauto using RReds.ProjCong.
apply rtc_once.
apply RRed.ProjPair.
+ move => p0 a2 a3 h0 [*]. subst.
move : iha hP' h0;repeat move/[apply].
hauto lq:on ctrs:rtc, ERed.R use:RReds.ProjCong.
hauto lq:on ctrs:rtc, EPar.R use:RReds.ProjCong.
- hauto lq:on inv:RRed.R.
Qed.
Lemma η_postponement_star n a b c :
@P n a ->
ERed.R a b ->
EPar.R a b ->
rtc RRed.R b c ->
exists d, rtc RRed.R a d /\ ERed.R d c.
exists d, rtc RRed.R a d /\ EPar.R d c.
Proof.
move => + + h. move : a.
elim : b c / h.
@ -1213,12 +1213,12 @@ Module UniqueNF (M : NoForbid) (MFacts : NoForbid_FactSig M).
Lemma η_postponement_star' n a b c :
@P n a ->
ERed.R a b ->
EPar.R a b ->
rtc RRed.R b c ->
exists d, rtc RRed.R a d /\ NeERed.R_nonelim d c.
exists d, rtc RRed.R a d /\ NeEPar.R_nonelim d c.
Proof.
move => h0 h1 h2.
have : exists d, rtc RRed.R a d /\ ERed.R d c by eauto using η_postponement_star.
have : exists d, rtc RRed.R a d /\ EPar.R d c by eauto using η_postponement_star.
move => [d [h3 /η_split]].
move /(_ ltac:(eauto using P_RReds)).
sfirstorder use:@relations.rtc_transitive.