1 (* Basic_1: was by definition: ty3_abst *)
2 (* Basic_2A1: was by definition: nta_ldec ntaa_ldec *)
5 (* Basic_1: was by definition: ty3_bind *)
6 (* Basic_2A1: was by definition: nta_bind ntaa_bind *)
9 (* Basic_2A1: was by definition: nta_pure ntaa_pure *)
12 (* Basic_1: was: ty3_gen_bind *)
13 (* Basic_2A1: was: nta_inv_bind1 ntaa_inv_bind1 *)
16 (* Basic_1: was: ty3_gen_lref *)
17 (* Basic_2A1: was: nta_inv_lref1 *)
18 lemma nta_inv_lref_sn_drops
20 (* Basic_1: uses: ty3_gen_abst_abst *)
23 (* Basic_1: uses: pc3_dec *)
26 (* Advanced properties ******************************************************)
28 | ntaa_cast: ∀L,T,U,W. ntaa h L T U → ntaa h L U W → ntaa h L (ⓝU. T) U
30 lemma nta_cast_alt: ∀h,L,T,W,U. ⦃h, L⦄ ⊢ T : W → ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ ⓝW.T : U.
31 #h #L #T #W #U #HTW #HTU
32 lapply (nta_mono … HTW … HTU) #HWU
33 elim (nta_fwd_correct … HTU) -HTU /3 width=3/
36 lemma nta_ind_alt: ∀h. ∀Q:lenv→relation term.
37 (∀L,k. Q L ⋆k ⋆(next h k)) →
39 ⇩[O, i] L ≡ K.ⓓV → ⦃h, K⦄ ⊢ V : W → ⇧[O, i + 1] W ≡ U →
43 ⇩[O, i] L ≡ K.ⓛW → ⦃h, K⦄ ⊢ W : V → ⇧[O, i + 1] W ≡ U →
47 ⦃h, L⦄ ⊢ V : W → ⦃h, L.ⓑ{I}V⦄ ⊢ T : U →
48 Q L V W → Q (L.ⓑ{I}V) T U → Q L (ⓑ{I}V.T) (ⓑ{I}V.U)
51 ⦃h, L⦄ ⊢ V : W → ⦃h, L⦄ ⊢ (ⓛW.T):(ⓛW.U) →
52 Q L V W →Q L (ⓛW.T) (ⓛW.U) →Q L (ⓐV.ⓛW.T) (ⓐV.ⓛW.U)
55 ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ (ⓐV.U) : W →
56 Q L T U → Q L (ⓐV.U) W → Q L (ⓐV.T) (ⓐV.U)
59 ⦃h, L⦄ ⊢ T : U → ⦃h, L⦄ ⊢ U : W →
60 Q L T U → Q L U W → Q L (ⓝU.T) U
63 ⦃h, L⦄ ⊢ T : U1 → L ⊢ U1 ⬌* U2 → ⦃h, L⦄ ⊢ U2 : V2 →
64 Q L T U1 →Q L U2 V2 →Q L T U2
66 ∀L,T,U. ⦃h, L⦄ ⊢ T : U → Q L T U.