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Add lemmas that bad forms are impossible

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Yiyun Liu 2025-01-29 22:25:14 -05:00
parent a47d69f427
commit aa2c2ca151
1 changed files with 27 additions and 2 deletions
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29
theories/fp_red.v
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@ -142,13 +142,32 @@ with TRedSN {n} : PTm n -> PTm n -> Prop :=
Derive Dependent Inversion tred_inv with (forall n (a b : PTm n), TRedSN a b) Sort Prop. Derive Dependent Inversion tred_inv with (forall n (a b : PTm n), TRedSN a b) Sort Prop.
Lemma PProjAbs_imp n p (a : PTm (S n)) :
~ SN (PProj p (PAbs a)).
Proof.
move E : (PProj p (PAbs a)) => u hu.
move : p a E.
elim : n u / hu=>//=.
hauto lq:on inv:SNe.
hauto lq:on inv:TRedSN.
Qed.
Lemma PProjPair_imp n (a b0 b1 : PTm n ) :
~ SN (PApp (PPair b0 b1) a).
Proof.
move E : (PApp (PPair b0 b1) a) => u hu.
move : a b0 b1 E.
elim : n u / hu=>//=.
hauto lq:on inv:SNe.
hauto lq:on inv:TRedSN.
Qed.
Scheme sne_ind := Induction for SNe Sort Prop Scheme sne_ind := Induction for SNe Sort Prop
with sn_ind := Induction for SN Sort Prop with sn_ind := Induction for SN Sort Prop
with sred_ind := Induction for TRedSN Sort Prop. with sred_ind := Induction for TRedSN Sort Prop.
Combined Scheme sn_mutual from sne_ind, sn_ind, sred_ind. Combined Scheme sn_mutual from sne_ind, sn_ind, sred_ind.
Fixpoint ne {n} (a : PTm n) := Fixpoint ne {n} (a : PTm n) :=
match a with match a with
| VarPTm i => true | VarPTm i => true
@ -797,8 +816,12 @@ Module SN_NoForbid : NoForbid.
Proof. hauto q:on use:red_sn_preservation, RPar.FromRRed. Qed. Proof. hauto q:on use:red_sn_preservation, RPar.FromRRed. Qed.
Lemma P_AppPair : forall n (a b c : PTm n), ~ P (PApp (PPair a b) c). Lemma P_AppPair : forall n (a b c : PTm n), ~ P (PApp (PPair a b) c).
Proof. Proof. sfirstorder use:PProjPair_imp. Qed.
Lemma P_ProjAbs : forall n p (a : PTm (S n)), ~ P (PProj p (PAbs a)).
Proof. sfirstorder use:PProjAbs_imp. Qed.
End SN_NoForbid.
Lemma bool_dec (a : bool) : a \/ ~~ a. Lemma bool_dec (a : bool) : a \/ ~~ a.
Proof. hauto lq:on inv:bool. Qed. Proof. hauto lq:on inv:bool. Qed.
@ -905,6 +928,8 @@ Proof.
- scongruence b:on. - scongruence b:on.
Qed. Qed.
Lemma η_nf'' n (a b : PTm n) : ERed'.R a b -> nf b -> nf a \/ rtc RRed.R a b. Lemma η_nf'' n (a b : PTm n) : ERed'.R a b -> nf b -> nf a \/ rtc RRed.R a b.
Proof. Proof.
move => h. move => h.