/2 width=3 by cpg_ess, ex2_intro/ qed.
lemma cpm_delta: ∀n,h,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 →
- â¬\86*[1] V2 â\89¡ W2 → ⦃G, K.ⓓV1⦄ ⊢ #0 ➡[n, h] W2.
+ â¬\86*[1] V2 â\89\98 W2 → ⦃G, K.ⓓV1⦄ ⊢ #0 ➡[n, h] W2.
#n #h #G #K #V1 #V2 #W2 *
/3 width=5 by cpg_delta, ex2_intro/
qed.
lemma cpm_ell: ∀n,h,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 →
- â¬\86*[1] V2 â\89¡ W2 → ⦃G, K.ⓛV1⦄ ⊢ #0 ➡[⫯n, h] W2.
+ â¬\86*[1] V2 â\89\98 W2 → ⦃G, K.ⓛV1⦄ ⊢ #0 ➡[⫯n, h] W2.
#n #h #G #K #V1 #V2 #W2 *
/3 width=5 by cpg_ell, ex2_intro, isrt_succ/
qed.
lemma cpm_lref: ∀n,h,I,G,K,T,U,i. ⦃G, K⦄ ⊢ #i ➡[n, h] T →
- â¬\86*[1] T â\89¡ U → ⦃G, K.ⓘ{I}⦄ ⊢ #⫯i ➡[n, h] U.
+ â¬\86*[1] T â\89\98 U → ⦃G, K.ⓘ{I}⦄ ⊢ #⫯i ➡[n, h] U.
#n #h #I #G #K #T #U #i *
/3 width=5 by cpg_lref, ex2_intro/
qed.
(* Basic_2A1: includes: cpr_zeta *)
lemma cpm_zeta: ∀n,h,G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ➡[n, h] T →
- â¬\86*[1] T2 â\89¡ T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡[n, h] T2.
+ â¬\86*[1] T2 â\89\98 T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡[n, h] T2.
#n #h #G #L #V #T1 #T #T2 *
/3 width=5 by cpg_zeta, isrt_plus_O2, ex2_intro/
qed.
(* Basic_2A1: includes: cpr_theta *)
lemma cpm_theta: ∀n,h,p,G,L,V1,V,V2,W1,W2,T1,T2.
- â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h] V â\86\92 â¬\86*[1] V â\89¡ V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 →
+ â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h] V â\86\92 â¬\86*[1] V â\89\98 V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 →
⦃G, L.ⓓW1⦄ ⊢ T1 ➡[n, h] T2 →
⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡[n, h] ⓓ{p}W2.ⓐV2.T2.
#n #h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #riV #rhV #HV1 #HV2 * #riW #rhW #HW12 *
lemma cpm_inv_atom1: ∀n,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[n, h] T2 →
∨∨ T2 = ⓪{J} ∧ n = 0
| ∃∃s. T2 = ⋆(next h s) & J = Sort s & n = 1
- | â\88\83â\88\83K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[n, 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¡[n, h] V2 & â¬\86*[1] V2 â\89\98 T2 &
L = K.ⓓV1 & J = LRef 0
- | â\88\83â\88\83k,K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[k, h] V2 & â¬\86*[1] V2 â\89¡ T2 &
+ | â\88\83â\88\83k,K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[k, h] V2 & â¬\86*[1] V2 â\89\98 T2 &
L = K.ⓛV1 & J = LRef 0 & n = ⫯k
- | â\88\83â\88\83I,K,T,i. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[n, h] T & â¬\86*[1] T â\89¡ T2 &
+ | â\88\83â\88\83I,K,T,i. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[n, h] T & â¬\86*[1] T â\89\98 T2 &
L = K.ⓘ{I} & J = LRef (⫯i).
#n #h #J #G #L #T2 * #c #Hc #H elim (cpg_inv_atom1 … H) -H *
[ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or5_intro0, conj/
lemma cpm_inv_zero1: ∀n,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[n, h] T2 →
∨∨ T2 = #0 ∧ n = 0
- | â\88\83â\88\83K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[n, 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¡[n, h] V2 & â¬\86*[1] V2 â\89\98 T2 &
L = K.ⓓV1
- | â\88\83â\88\83k,K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[k, h] V2 & â¬\86*[1] V2 â\89¡ T2 &
+ | â\88\83â\88\83k,K,V1,V2. â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡[k, h] V2 & â¬\86*[1] V2 â\89\98 T2 &
L = K.ⓛV1 & n = ⫯k.
#n #h #G #L #T2 * #c #Hc #H elim (cpg_inv_zero1 … H) -H *
[ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or3_intro0, conj/
lemma cpm_inv_lref1: ∀n,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[n, h] T2 →
∨∨ T2 = #(⫯i) ∧ n = 0
- | â\88\83â\88\83I,K,T. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[n, h] T & â¬\86*[1] T â\89¡ T2 & L = K.ⓘ{I}.
+ | â\88\83â\88\83I,K,T. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[n, h] T & â¬\86*[1] T â\89\98 T2 & L = K.ⓘ{I}.
#n #h #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1 … H) -H *
[ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or_introl, conj/
| #I #K #V2 #HV2 #HVT2 #H destruct
lemma cpm_inv_bind1: ∀n,h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[n, h] U2 →
∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[n, h] T2 &
U2 = ⓑ{p,I}V2.T2
- | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[n, h] T & â¬\86*[1] U2 â\89¡ T &
+ | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[n, h] T & â¬\86*[1] U2 â\89\98 T &
p = true & I = Abbr.
#n #h #p #I #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_bind1 … H) -H *
[ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
lemma cpm_inv_abbr1: ∀n,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ➡[n, h] U2 →
∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[n, h] T2 &
U2 = ⓓ{p}V2.T2
- | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[n, h] T & â¬\86*[1] U2 â\89¡ T & p = true.
+ | â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[n, h] T & â¬\86*[1] U2 â\89\98 T & p = true.
#n #h #p #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_abbr1 … H) -H *
[ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
elim (isrt_inv_max … Hc) -Hc #nV #nT #HcV #HcT #H destruct
| ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 &
⦃G, L.ⓛW1⦄ ⊢ T1 ➡[n, h] T2 &
U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2
- | 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 ➡[n, h] T2 &
U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2.
#n #h #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_appl1 … H) -H *