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Write down the statement of pair_epar

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Yiyun Liu 2024-12-22 12:12:25 -05:00
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theories/fp_red.v
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@ -364,6 +364,16 @@ Proof.
apply rtc_once. apply : RPar.ProjAbs; eauto using RPar.refl.
Qed.
Lemma Pair_EPar n (a b c : Tm n) :
EPar.R (Pair a b) c ->
(forall p, exists d, rtc RPar.R (Proj p c) d /\ EPar.R (if p is PL then a else b) d) /\
(exists d0 d1, rtc RPar.R (App (ren_Tm shift c) (VarTm var_zero))
(Pair (App (ren_Tm shift d0) (VarTm var_zero))(App (ren_Tm shift d1) (VarTm var_zero))) /\
EPar.R a d0 /\ EPar.R b d1).
Proof.
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.