yiyunliu/pair-eta
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Work on Abs_EPar

Browse source
This commit is contained in:
Yiyun Liu 2024-12-17 01:55:28 -05:00
parent a285b44a46
commit 9dda22dae2
1 changed files with 37 additions and 2 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

39
theories/fp_red.v
View file

@ -36,7 +36,7 @@ Module Par.
R a0 (Abs (App (ren_Tm shift a1) (VarTm var_zero)))
| PairEta a0 a1 :
R a0 a1 ->
R a0 (Pair a1 a1)
R a0 (Pair (Proj1 a1) (Proj2 a1))
(*************** Congruence ********************)
| Var i : R (VarTm i) (VarTm i)
@ -138,7 +138,7 @@ Module EPar.
R a0 (Abs (App (ren_Tm shift a1) (VarTm var_zero)))
| PairEta a0 a1 :
R a0 a1 ->
R a0 (Pair a1 a1)
R a0 (Pair (Proj1 a1) (Proj2 a1))
(*************** Congruence ********************)
| Var i : R (VarTm i) (VarTm i)
@ -240,6 +240,41 @@ Proof.
- hauto lq:on ctrs:rtc inv:RPar.R, rtc.
Qed.
Lemma Abs_EPar n a (b : Tm n) :
EPar.R (Abs a) b ->
forall c, exists d,
EPar.R (subst_Tm (scons c VarTm) a) d /\
rtc RPar.R (App b c) 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.
Admitted.
Lemma commutativity n (a b0 b1 : Tm n) :
EPar.R a b0 -> RPar.R a b1 -> exists c, rtc RPar.R b0 c /\ EPar.R b1 c.
Proof.