∨∨ T2 = ⓪{J}
| ∃∃K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 & ⬆*[1] V2 ≡ T2 &
L = K.ⓓV1 & J = LRef 0
- | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 &
- L = K.ⓑ{I}V & J = LRef (⫯i).
+ | ∃∃I,K,T,i. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 &
+ L = K.ⓘ{I} & J = LRef (⫯i).
#h #J #G #L #T2 #H elim (cpm_inv_atom1 … H) -H *
-/3 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex4_3_intro/
-[ #n #_ #_ #H destruct
-| #n #K #V1 #V2 #_ #_ #_ #_ #H destruct
-]
+/3 width=8 by tri_lt, or3_intro0, or3_intro1, or3_intro2, ex4_4_intro, ex4_3_intro/
+#n #_ #_ #H destruct
qed-.
(* Basic_1: includes: pr0_gen_sort pr2_gen_sort *)
qed-.
lemma cpr_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[h] T2 →
- T2 = #0 ∨
- ∃∃K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 & ⬆*[1] V2 ≡ T2 &
- L = K.ⓓV1.
+ ∨∨ T2 = #0
+ | ∃∃K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 & ⬆*[1] V2 ≡ T2 &
+ L = K.ⓓV1.
#h #G #L #T2 #H elim (cpm_inv_zero1 … H) -H *
/3 width=6 by ex3_3_intro, or_introl, or_intror/
#n #K #V1 #V2 #_ #_ #_ #H destruct
qed-.
lemma cpr_inv_lref1: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[h] T2 →
- T2 = #(⫯i) ∨
- ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V.
+ ∨∨ T2 = #(⫯i)
+ | ∃∃I,K,T. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 & L = K.ⓘ{I}.
#h #G #L #T2 #i #H elim (cpm_inv_lref1 … H) -H *
-/3 width=7 by ex3_4_intro, or_introl, or_intror/
+/3 width=6 by ex3_3_intro, or_introl, or_intror/
qed-.
lemma cpr_inv_gref1: ∀h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[h] T2 → T2 = §l.
qed-.
(* Basic_1: includes: pr0_gen_cast pr2_gen_cast *)
-lemma cpr_inv_cast1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝ V1. U1 ➡[h] U2 → (
- ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[h] T2 &
- U2 = ⓝV2.T2
- ) ∨ ⦃G, L⦄ ⊢ U1 ➡[h] U2.
+lemma cpr_inv_cast1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝ V1.U1 ➡[h] U2 →
+ â\88¨â\88¨ â\88\83â\88\83V2,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h] V2 & â¦\83G, Lâ¦\84 â\8a¢ U1 â\9e¡[h] T2 &
+ U2 = ⓝV2.T2
+ | ⦃G, L⦄ ⊢ U1 ➡[h] U2.
#h #G #L #V1 #U1 #U2 #H elim (cpm_inv_cast1 … H) -H
/2 width=1 by or_introl, or_intror/ * #n #_ #H destruct
qed-.