(* Note: this means that no type is a universe *)
lemma nta_fwd_aaa (h) (a) (G) (L):
- â\88\80T,U. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U â\86\92 â\88\83â\88\83A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A & â\9dªG,Lâ\9d« ⊢ U ⁝ A.
+ â\88\80T,U. â\9d¨G,Lâ\9d© â\8a¢ T :[h,a] U â\86\92 â\88\83â\88\83A. â\9d¨G,Lâ\9d© â\8a¢ T â\81\9d A & â\9d¨G,Lâ\9d© ⊢ U ⁝ A.
#h #a #G #L #T #U #H
elim (cnv_fwd_aaa … H) -H #A #H
elim (aaa_inv_cast … H) -H #HU #HT
(* Basic_1: uses: ty3_predicative *)
lemma nta_abst_predicative (h) (a) (p) (G) (L):
- â\88\80W,T. â\9dªG,Lâ\9d« ⊢ ⓛ[p]W.T :[h,a] W → ⊥.
+ â\88\80W,T. â\9d¨G,Lâ\9d© ⊢ ⓛ[p]W.T :[h,a] W → ⊥.
#h #a #p #G #L #W #T #H
elim (nta_fwd_aaa … H) -a -h #X #H #H1W
elim (aaa_inv_abst … H) -p #B #A #H2W #_ #H destruct -T
(* Basic_1: uses: ty3_repellent *)
theorem nta_abst_repellent (h) (a) (p) (G) (K):
- â\88\80W,T,U1. â\9dªG,Kâ\9d« ⊢ ⓛ[p]W.T :[h,a] U1 →
- â\88\80U2. â\9dªG,K.â\93\9bWâ\9d« ⊢ T :[h,a] U2 → ⇧[1] U1 ≘ U2 → ⊥.
+ â\88\80W,T,U1. â\9d¨G,Kâ\9d© ⊢ ⓛ[p]W.T :[h,a] U1 →
+ â\88\80U2. â\9d¨G,K.â\93\9bWâ\9d© ⊢ T :[h,a] U2 → ⇧[1] U1 ≘ U2 → ⊥.
#h #a #p #G #K #W #T #U1 #H1 #U2 #H2 #HU12
elim (nta_fwd_aaa … H2) -H2 #A2 #H2T #H2U2
elim (nta_fwd_aaa … H1) -H1 #X1 #H1 #HU1