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par eta is too complex

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Yiyun Liu 2024-12-20 16:19:35 -05:00
parent 9dda22dae2
commit 67bcc69de7
1 changed files with 46 additions and 30 deletions
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76
theories/fp_red.v
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@ -242,36 +242,49 @@ Qed.
Lemma Abs_EPar n a (b : Tm n) :
EPar.R (Abs a) b ->
forall c, exists d,
(forall c m (ξ : fin n -> fin m), exists d,
EPar.R (subst_Tm (scons c VarTm) a) d /\
rtc RPar.R (App b c) d.
rtc RPar.R (App b c) d) /\
(exists d,
EPar.R a d /\
rtc RPar.R (Proj1 b) (Abs (Proj1 d)) /\
rtc RPar.R (Proj2 b) (Abs (Proj2 d))).
Proof.
move E : (Abs a) => u h.
move : a E.
elim : n u b /h => //=.
- move => n a0 a1 ha iha b ? c. subst.
specialize iha with (1 := eq_refl) (c := c).
move : iha => [d [ih0 ih1]].
exists d.
split => //.
apply : rtc_l.
apply RPar.AppAbs; eauto => //=.
apply RPar.refl.
by apply RPar.refl.
by asimpl.
- move => n a0 a1 ha iha a ? c. subst.
specialize iha with (1 := eq_refl) (c := c).
move : iha => [d [ih0 ih1]].
exists (Pair (Proj1 d) (Proj2 d)). split => //.
+ move { ih1}.
hauto lq:on ctrs:EPar.R.
+ apply : rtc_l.
apply RPar.AppPair.
admit.
admit.
apply RPar.refl.
admit.
- admit.
(* move E : (Abs a) => u h. *)
(* move : a E. *)
(* elim : n u b /h => //=. *)
(* - move => n a0 a1 ha iha b ?. subst. *)
(* split. *)
(* + move => c. *)
(* specialize iha with (1 := eq_refl). *)
(* move : iha => [+ _]. move /(_ c) => [d [ih0 ih1]]. *)
(* exists d. *)
(* split => //. *)
(* apply : rtc_l. *)
(* apply RPar.AppAbs; eauto => //=. *)
(* apply RPar.refl. *)
(* by apply RPar.refl. *)
(* by asimpl. *)
(* + specialize iha with (1 := eq_refl). *)
(* move : iha => [_ [d [ih0 [ih1 ih2]]]]. *)
(* exists d. *)
(* repeat split => //. *)
(* * apply : rtc_l. apply : RPar.Proj1Abs. apply RPar.refl. *)
(* apply : RPars_AbsCong. *)
(* apply *)
(* - move => n a0 a1 ha iha a ? c. subst. *)
(* specialize iha with (1 := eq_refl) (c := c). *)
(* move : iha => [d [ih0 ih1]]. *)
(* exists (Pair (Proj1 d) (Proj2 d)). split => //. *)
(* + move { ih1}. *)
(* hauto lq:on ctrs:EPar.R. *)
(* + apply : rtc_l. *)
(* apply RPar.AppPair. *)
(* admit. *)
(* admit. *)
(* apply RPar.refl. *)
(* admit. *)
(* - admit. *)
Admitted.
@ -289,8 +302,8 @@ Proof.
+ hauto lq:on ctrs:EPar.R use:EPar.refl, EPar.renaming.
- move => n a b0 hb0 ihb0 b1 /[dup] hb1 {}/ihb0.
move => [c [ih0 ih1]].
exists (Pair c c). split.
+ by apply RPars_PairCong.
exists (Pair (Proj1 c) (Proj2 c)). split.
+ apply RPars_PairCong; admit.
+ hauto lq:on ctrs:EPar.R use:EPar.refl, EPar.renaming.
- hauto l:on ctrs:rtc inv:RPar.R.
- move => n a0 a1 h ih b1.
@ -300,6 +313,9 @@ Proof.
- move => n a0 a1 b0 b1 ha iha hb ihb b2.
elim /RPar.inv => //= _.
+ move => a2 a3 b3 b4 h0 h1 [*]. subst.
have {}/iha : RPar.R (Abs a2) (Abs a3) by hauto lq:on ctrs:RPar.R.
move => [c [ih0 ih1]].
elim /EPar.inv : ha => //= _.
* move => a0 a4 h *. subst.
move /ihb : h1 {ihb}.