lemma cpr_inv_atom1: ∀h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[h] T2 →
∨∨ T2 = ⓪{J}
- | â\88\83â\88\83K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[h] V2 & â¬\86*[1] V2 â\89¡ T2 &
+ | â\88\83â\88\83K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[h] V2 & â¬\86*[1] V2 â\89\98 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-.
| ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 &
⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h] T2 & U1 = ⓛ{p}W1.T1 &
U2 = ⓓ{p}ⓝW2.V2.T2 & I = Appl
- | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h] V & â¬\86*[1] V â\89¡ V2 &
+ | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h] V & â¬\86*[1] V â\89\98 V2 &
⦃G, L⦄ ⊢ W1 ➡[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h] T2 &
U1 = ⓓ{p}W1.T1 &
U2 = ⓓ{p}W2.ⓐV2.T2 & I = Appl.
pr2_gen_csort pr2_gen_cflat pr2_gen_cbind
pr2_gen_ctail pr2_ctail
*)
-(* Basic_1: removed local theorems 4:
- pr0_delta_eps pr0_cong_delta
- pr2_free_free pr2_free_delta
-*)