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
- | â\88\83â\88\83I,K,T,i. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[h] T & â¬\86*[1] T â\89¡ T2 &
- L = K.â\93\98{I} & J = LRef (⫯i).
+ | â\88\83â\88\83I,K,T,i. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[h] T & â¬\86*[1] T â\89\98 T2 &
+ L = K.â\93\98{I} & J = LRef (â\86\91i).
#h #J #G #L #T2 #H elim (cpm_inv_atom1 … H) -H *
/3 width=8 by tri_lt, or3_intro0, or3_intro1, or3_intro2, ex4_4_intro, ex4_3_intro/
#n #_ #_ #H destruct
lemma cpr_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[h] T2 →
∨∨ T2 = #0
- | 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.
#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: â\88\80h,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #⫯i ➡[h] T2 →
- â\88¨â\88¨ T2 = #(⫯i)
- | â\88\83â\88\83I,K,T. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[h] T & â¬\86*[1] T â\89¡ T2 & L = K.ⓘ{I}.
+lemma cpr_inv_lref1: â\88\80h,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #â\86\91i ➡[h] T2 →
+ â\88¨â\88¨ T2 = #(â\86\91i)
+ | â\88\83â\88\83I,K,T. â¦\83G, Kâ¦\84 â\8a¢ #i â\9e¡[h] T & â¬\86*[1] T â\89\98 T2 & L = K.ⓘ{I}.
#h #G #L #T2 #i #H elim (cpm_inv_lref1 … H) -H *
/3 width=6 by ex3_3_intro, or_introl, or_intror/
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.