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Finish morphing_SemWt

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Yiyun Liu 2025-02-24 15:20:30 -05:00
parent 9cb7f31cdb
commit 1effbd3d85
2 changed files with 174 additions and 103 deletions
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17
theories/fp_red.v
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@ -2969,6 +2969,14 @@ Module DJoin.
R (PBind p A0 B0) (PBind p A1 B1).
Proof. hauto q:on use:REReds.BindCong. Qed.
Lemma IndCong n P0 P1 (a0 a1 : PTm n) b0 b1 c0 c1 :
R P0 P1 ->
R a0 a1 ->
R b0 b1 ->
R c0 c1 ->
R (PInd P0 a0 b0 c0) (PInd P1 a1 b1 c1).
Proof. hauto q:on use:REReds.IndCong. Qed.
Lemma FromRedSNs n (a b : PTm n) :
rtc TRedSN a b ->
R a b.
@ -3129,6 +3137,15 @@ Module DJoin.
hauto q:on ctrs:rtc inv:option use:REReds.cong.
Qed.
Lemma cong' n m (a b : PTm (S n)) c d (ρ : fin n -> PTm m) :
R a b ->
R c d -> R (subst_PTm (scons c ρ) a) (subst_PTm (scons d ρ) b).
Proof.
rewrite /R. move => [ab [h2 h3]] [cd [h0 h1]].
exists (subst_PTm (scons cd ρ) ab).
hauto q:on ctrs:rtc inv:option use:REReds.cong'.
Qed.
Lemma pair_inj n (a0 a1 b0 b1 : PTm n) :
SN (PPair a0 b0) ->
SN (PPair a1 b1) ->