| snv_bind: ∀a,I,L,V,T. snv h g L V → snv h g (L.ⓑ{I}V) T → snv h g L (ⓑ{a,I}V.T)
| snv_appl: ∀a,L,V,W,W0,T,U,l. snv h g L V → snv h g L T →
⦃h, L⦄ ⊢ V •[g, l + 1] W → L ⊢ W ➡* W0 →
- â¦\83h, Lâ¦\84 â\8a¢ T â\9e¸*[g] ⓛ{a}W0.U → snv h g L (ⓐV.T)
+ â¦\83h, Lâ¦\84 â\8a¢ T â\80¢â\9e¡*[g] ⓛ{a}W0.U → snv h g L (ⓐV.T)
| snv_cast: ∀L,W,T,U,l. snv h g L W → snv h g L T →
⦃h, L⦄ ⊢ T •[g, l + 1] U → L ⊢ W ⬌* U → snv h g L (ⓝW.T)
.
fact snv_inv_appl_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀V,T. X = ⓐV.T →
∃∃a,W,W0,U,l. ⦃h, L⦄ ⊩ V :[g] & ⦃h, L⦄ ⊩ T :[g] &
⦃h, L⦄ ⊢ V •[g, l + 1] W & L ⊢ W ➡* W0 &
- â¦\83h, Lâ¦\84 â\8a¢ T â\9e¸*[g] ⓛ{a}W0.U.
+ â¦\83h, Lâ¦\84 â\8a¢ T â\80¢â\9e¡*[g] ⓛ{a}W0.U.
#h #g #L #X * -L -X
[ #L #k #V #T #H destruct
| #I #L #K #V0 #i #_ #_ #V #T #H destruct
lemma snv_inv_appl: ∀h,g,L,V,T. ⦃h, L⦄ ⊩ ⓐV.T :[g] →
∃∃a,W,W0,U,l. ⦃h, L⦄ ⊩ V :[g] & ⦃h, L⦄ ⊩ T :[g] &
⦃h, L⦄ ⊢ V •[g, l + 1] W & L ⊢ W ➡* W0 &
- â¦\83h, Lâ¦\84 â\8a¢ T â\9e¸*[g] ⓛ{a}W0.U.
+ â¦\83h, Lâ¦\84 â\8a¢ T â\80¢â\9e¡*[g] ⓛ{a}W0.U.
/2 width=3/ qed-.
fact snv_inv_cast_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀W,T. X = ⓝW.T →