(* Basic_1: was only: sn3_appls_lref *)
lemma csn_applv_cnf: ∀L,T. 𝐒⦃T⦄ → L ⊢ 𝐍⦃T⦄ →
- â\88\80Vs. L â\8a¢ â¬\87* Vs â\86\92 L â\8a¢ â¬\87* ⒶVs.T.
+ â\88\80Vs. L â\8a¢ â¬\8a* Vs â\86\92 L â\8a¢ â¬\8a* ⒶVs.T.
#L #T #H1T #H2T #Vs elim Vs -Vs [ #_ @(csn_cnf … H2T) ] (**) (* /2 width=1/ does not work *)
#V #Vs #IHV #H
elim (csnv_inv_cons … H) -H #HV #HVs
qed.
(* Basic_1: was: sn3_appls_beta *)
-lemma csn_applv_beta: ∀L,W. L ⊢ ⬇* W →
- â\88\80Vs,V,T. L â\8a¢ â¬\87* â\92¶Vs.â\93\93V.T →
- L â\8a¢ â¬\87* â\92¶Vs. â\93\90V.â\93\9bW. T.
-#L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
+lemma csn_applv_beta: ∀a,L,W. L ⊢ ⬊* W →
+ â\88\80Vs,V,T. L â\8a¢ â¬\8a* â\92¶Vs.â\93\93{a}V.T →
+ L â\8a¢ â¬\8a* â\92¶Vs. â\93\90V.â\93\9b{a}W. T.
+#a #L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
#V0 #Vs #IHV #V #T #H1T
lapply (csn_fwd_pair_sn … H1T) #HV0
lapply (csn_fwd_flat_dx … H1T) #H2T
lemma csn_applv_delta: ∀L,K,V1,i. ⇩[0, i] L ≡ K. ⓓV1 →
∀V2. ⇧[0, i + 1] V1 ≡ V2 →
- â\88\80Vs.L â\8a¢ â¬\87* (â\92¶Vs. V2) â\86\92 L â\8a¢ â¬\87* (ⒶVs. #i).
+ â\88\80Vs.L â\8a¢ â¬\8a* (â\92¶Vs. V2) â\86\92 L â\8a¢ â¬\8a* (ⒶVs. #i).
#L #K #V1 #i #HLK #V2 #HV12 #Vs elim Vs -Vs
[ #H
lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
qed.
(* Basic_1: was: sn3_appls_abbr *)
-lemma csn_applv_theta: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
- â\88\80V,T. L â\8a¢ â¬\87* â\93\93V. â\92¶V2s. T â\86\92 L â\8a¢ â¬\87* V →
- L â\8a¢ â¬\87* â\92¶V1s. â\93\93V. T.
-#L #V1s #V2s * -V1s -V2s /2 width=1/
+lemma csn_applv_theta: ∀a,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+ â\88\80V,T. L â\8a¢ â¬\8a* â\93\93{a}V. â\92¶V2s. T â\86\92 L â\8a¢ â¬\8a* V →
+ L â\8a¢ â¬\8a* â\92¶V1s. â\93\93{a}V. T.
+#a #L #V1s #V2s * -V1s -V2s /2 width=1/
#V1s #V2s #V1 #V2 #HV12 #H
generalize in match HV12; -HV12 generalize in match V2; -V2 generalize in match V1; -V1
elim H -V1s -V2s /2 width=3/
qed.
(* Basic_1: was: sn3_appls_cast *)
-lemma csn_applv_tau: â\88\80L,W. L â\8a¢ â¬\87* W →
- â\88\80Vs,T. L â\8a¢ â¬\87* ⒶVs. T →
- L â\8a¢ â¬\87* ⒶVs. ⓝW. T.
+lemma csn_applv_tau: â\88\80L,W. L â\8a¢ â¬\8a* W →
+ â\88\80Vs,T. L â\8a¢ â¬\8a* ⒶVs. T →
+ L â\8a¢ â¬\8a* ⒶVs. ⓝW. T.
#L #W #HW #Vs elim Vs -Vs /2 width=1/ -HW
#V #Vs #IHV #T #H1T
lapply (csn_fwd_pair_sn … H1T) #HV
]
qed.
-theorem csn_acr: acr cpr (eq â\80¦) (csn â\80¦) (λL,T. L â\8a¢ â¬\87* T).
+theorem csn_acr: acr cpr (eq â\80¦) (csn â\80¦) (λL,T. L â\8a¢ â¬\8a* T).
@mk_acr //
[ /3 width=1/
| /2 width=1/
| /2 width=6/
-| #L #V1 #V2 #HV12 #V #T #H #HVT
+| #L #V1 #V2 #HV12 #a #V #T #H #HVT
@(csn_applv_theta … HV12) -HV12 //
@(csn_abbr) //
| /2 width=1/