/3 width=5 by cpg_appl, cpg_cast, ex_intro/
qed.
-lemma cpx_zeta: ∀h,G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ⬈[h] T →
- ⬆*[1] T2 ≘ T → ⦃G, L⦄ ⊢ +ⓓV.T1 ⬈[h] T2.
-#h #G #L #V #T1 #T #T2 *
+lemma cpx_zeta (h) (G) (L):
+ ∀T1,T. ⬆*[1] T ≘ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬈[h] T2 →
+ ∀V. ⦃G, L⦄ ⊢ +ⓓV.T1 ⬈[h] T2.
+#h #G #L #T1 #T #HT1 #T2 *
/3 width=4 by cpg_zeta, ex_intro/
qed.
lemma cpx_inv_bind1: ∀h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] U2 →
∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 &
U2 = ⓑ{p,I}V2.T2
- | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â¬\88[h] T & â¬\86*[1] U2 â\89\98 T &
+ | â\88\83â\88\83T. â¬\86*[1] T â\89\98 T1 & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88[h] U2 &
p = true & I = Abbr.
#h #p #I #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_bind1 … H) -H *
/4 width=5 by ex4_intro, ex3_2_intro, ex_intro, or_introl, or_intror/
lemma cpx_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈[h] U2 →
∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[h] T2 &
U2 = ⓓ{p}V2.T2
- | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â¬\88[h] T & â¬\86*[1] U2 â\89\98 T & p = true.
+ | â\88\83â\88\83T. â¬\86*[1] T â\89\98 T1 & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88[h] U2 & p = true.
#h #p #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_abbr1 … H) -H *
/4 width=5 by ex3_2_intro, ex3_intro, ex_intro, or_introl, or_intror/
qed-.
Q G L V1 V2 → Q G (L.ⓑ{I}V1) T1 T2 → Q G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2)
) → (∀I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
Q G L V1 V2 → Q G L T1 T2 → Q G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
- ) â\86\92 (â\88\80G,L,V,T1,T,T2. â¦\83G, L.â\93\93Vâ¦\84 â\8a¢ T1 â¬\88[h] T â\86\92 Q G (L.â\93\93V) T1 T →
- ⬆*[1] T2 ≘ T → Q G L (+ⓓV.T1) T2
+ ) â\86\92 (â\88\80G,L,V,T1,T,T2. â¬\86*[1] T â\89\98 T1 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T â¬\88[h] T2 â\86\92 Q G L T T2 →
+ Q G L (+ⓓV.T1) T2
) → (∀G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → Q G L T1 T2 →
Q G L (ⓝV.T1) T2
) → (∀G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → Q G L V1 V2 →