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Yiyun Liu 2024-12-25 13:15:52 -05:00
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commit 2b26735fff
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19
theories/fp_red.v
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@ -227,6 +227,18 @@ Module Pars.
induction 1; hauto l:on ctrs:rtc use:Par.substing.
Qed.
Lemma antirenaming n m (a : Tm n) (b : Tm m) (ξ : fin n -> fin m) :
rtc Par.R (ren_Tm ξ a) b -> exists b0, rtc Par.R a b0 /\ ren_Tm ξ b0 = b.
Proof.
move E :(ren_Tm ξ a) => u h.
move : a E.
elim : u b /h.
- sfirstorder.
- move => a b c h0 h1 ih1 a0 ?. subst.
move /Par.antirenaming : h0.
move => [b0 [h2 ?]]. subst.
hauto lq:on rew:off ctrs:rtc.
Qed.
End Pars.
(***************** Beta rules only ***********************)
@ -1149,10 +1161,11 @@ Proof.
simp extract.
move => [A0][B0][h0][h1]h2.
(* anti renaming for par *)
have : exists A1, rtc Par.R A A1 /\ ren_Tm shift A1 = A0 by admit.
have : exists A1, rtc Par.R A A1 /\ ren_Tm shift A1 = A0
by hauto l:on use:Pars.antirenaming.
move => [A1 [h3 h4]].
have : exists B1, rtc Par.R B B1 /\ ren_Tm (upRen_Tm_Tm shift) B1 = B0
by admit.
by hauto l:on use:Pars.antirenaming.
move => [B1 [h5 h6]].
subst.
have {}h0 : subst_Tm (scons Bot VarTm) (extract a) =
@ -1163,7 +1176,7 @@ Proof.
- hauto l:on rew:db:prov, extract.
- hauto l:on rew:db:prov, extract.
- qauto l:on rew:db:prov, extract.
Admitted.
Qed.
Lemma pi_inv n (A : Tm n) B C :
rtc Par.R (Pi A B) C ->