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Yiyun Liu 2025-02-03 22:47:49 -05:00
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53
theories/fp_red.v
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@ -1434,6 +1434,7 @@ Module EReds.
apply PairCong; eauto using ProjCong.
apply ERed.PairEta.
Qed.
End EReds.
#[export]Hint Constructors ERed.R RRed.R EPar.R : red.
@ -1519,6 +1520,35 @@ Module REReds.
rtc RERed.R a b.
Proof. induction 1; hauto lq:on ctrs:rtc use:RERed.FromEta. Qed.
#[local]Ltac solve_s_rec :=
move => *; eapply rtc_l; eauto;
hauto lq:on ctrs:RERed.R.
#[local]Ltac solve_s :=
repeat (induction 1; last by solve_s_rec); apply rtc_refl.
Lemma AbsCong n (a b : PTm (S n)) :
rtc RERed.R a b ->
rtc RERed.R (PAbs a) (PAbs b).
Proof. solve_s. Qed.
Lemma AppCong n (a0 a1 b0 b1 : PTm n) :
rtc RERed.R a0 a1 ->
rtc RERed.R b0 b1 ->
rtc RERed.R (PApp a0 b0) (PApp a1 b1).
Proof. solve_s. Qed.
Lemma PairCong n (a0 a1 b0 b1 : PTm n) :
rtc RERed.R a0 a1 ->
rtc RERed.R b0 b1 ->
rtc RERed.R (PPair a0 b0) (PPair a1 b1).
Proof. solve_s. Qed.
Lemma ProjCong n p (a0 a1 : PTm n) :
rtc RERed.R a0 a1 ->
rtc RERed.R (PProj p a0) (PProj p a1).
Proof. solve_s. Qed.
End REReds.
Module LoRed.
@ -1861,4 +1891,27 @@ Module DJoin.
move => [v [h0 h1]].
exists v. sfirstorder use:@relations.rtc_transitive.
Qed.
Lemma AbsCong n (a b : PTm (S n)) :
R a b ->
R (PAbs a) (PAbs b).
Proof. hauto lq:on use:REReds.AbsCong unfold:R. Qed.
Lemma AppCong n (a0 a1 b0 b1 : PTm n) :
R a0 a1 ->
R b0 b1 ->
R (PApp a0 b0) (PApp a1 b1).
Proof. hauto lq:on use:REReds.AppCong unfold:R. Qed.
Lemma PairCong n (a0 a1 b0 b1 : PTm n) :
R a0 a1 ->
R b0 b1 ->
R (PPair a0 b0) (PPair a1 b1).
Proof. hauto q:on use:REReds.PairCong. Qed.
Lemma ProjCong n p (a0 a1 : PTm n) :
R a0 a1 ->
R (PProj p a0) (PProj p a1).
Proof. hauto q:on use:REReds.ProjCong. Qed.
End DJoin.