(* Basic_2A1: uses by definition nta_appl ntaa_appl *)
lemma nta_appl_abst (h) (a) (p) (G) (L):
∀n. ad a n →
- â\88\80V,W. â¦\83G,Lâ¦\84 ⊢ V :[h,a] W →
- â\88\80T,U. â¦\83G,L.â\93\9bWâ¦\84 â\8a¢ T :[h,a] U â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.â\93\9b{p}W.T :[h,a] â\93\90V.â\93\9b{p}W.U.
+ â\88\80V,W. â\9dªG,Lâ\9d« ⊢ V :[h,a] W →
+ â\88\80T,U. â\9dªG,L.â\93\9bWâ\9d« â\8a¢ T :[h,a] U â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\93\90V.â\93\9b[p]W.T :[h,a] â\93\90V.â\93\9b[p]W.U.
#h #a #p #G #L #n #Ha #V #W #H1 #T #U #H2
elim (cnv_inv_cast … H1) -H1 #X1 #HW #HV #HWX1 #HVX1
elim (cnv_inv_cast … H2) -H2 #X2 #HU #HT #HUX2 #HTX2
(* Basic_2A1: was nta_appl_old *)
lemma nta_appl (h) (a) (p) (G) (L):
∀n. 1 ≤ n → ad a n →
- â\88\80V,W. â¦\83G,Lâ¦\84 ⊢ V :[h,a] W →
- â\88\80T,U. â¦\83G,Lâ¦\84 â\8a¢ T :[h,a] â\93\9b{p}W.U â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.T :[h,a] â\93\90V.â\93\9b{p}W.U.
+ â\88\80V,W. â\9dªG,Lâ\9d« ⊢ V :[h,a] W →
+ â\88\80T,U. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] â\93\9b[p]W.U â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\93\90V.T :[h,a] â\93\90V.â\93\9b[p]W.U.
#h #a #p #G #L #n #Hn #Ha #V #W #H1 #T #U #H2
elim (cnv_inv_cast … H1) -H1 #X1 #HW #HV #HWX1 #HVX1
elim (cnv_inv_cast … H2) -H2 #X2 #HU #HT #HUX2 #HTX2
elim (cpms_inv_abst_sn … HUX2) #W0 #U0 #HW0 #HU0 #H destruct
elim (cprs_conf … HWX1 … HW0) -HW0 #X0 #HX10 #HWX0
-@(cnv_cast … (ⓐV.ⓛ{p}W0.U0)) (**) (* full auto too slow *)
+@(cnv_cast … (ⓐV.ⓛ[p]W0.U0)) (**) (* full auto too slow *)
[ /2 width=11 by cnv_appl_ge/
| /3 width=11 by cnv_appl_ge, cpms_cprs_trans/
| /2 width=1 by cpms_appl_dx/
(* Inversion lemmas with advanced rt_computation for terms ******************)
lemma nta_inv_abst_bi_cnv (h) (a) (p) (G) (K) (W):
- â\88\80T,U. â¦\83G,Kâ¦\84 â\8a¢ â\93\9b{p}W.T :[h,a] â\93\9b{p}W.U →
- â\88§â\88§ â¦\83G,Kâ¦\84 â\8a¢ W ![h,a] & â¦\83G,K.â\93\9bWâ¦\84 ⊢ T :[h,a] U.
+ â\88\80T,U. â\9dªG,Kâ\9d« â\8a¢ â\93\9b[p]W.T :[h,a] â\93\9b[p]W.U →
+ â\88§â\88§ â\9dªG,Kâ\9d« â\8a¢ W ![h,a] & â\9dªG,K.â\93\9bWâ\9d« ⊢ T :[h,a] U.
#h #a #p #G #K #W #T #U #H
elim (cnv_inv_cast … H) -H #X #HWU #HWT #HUX #HTX
elim (cnv_inv_bind … HWU) -HWU #HW #HU