- ground_2: support for lifts_div4

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpg.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
index 12c45c9feea984308225a25786098c9c342e9e92..22c671d90e4aeb3afeb82a2ff73b5bcd34905a8a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
@@ -30,7 +30,7 @@ inductive cpg (h): rtc → relation4 genv lenv term term ≝
              ⬆*[1] V2 ≡ W2 → cpg h (↓c) G (L.ⓓV1) (#0) W2
 | cpg_ell  : ∀c,G,L,V1,V2,W2. cpg h c G L V1 V2 →
              ⬆*[1] V2 ≡ W2 → cpg h ((↓c)+𝟘𝟙) G (L.ⓛV1) (#0) W2
-| cpt_lref : ∀c,I,G,L,V,T,U,i. cpg h c G L (#i) T → 
+| cpg_lref : ∀c,I,G,L,V,T,U,i. cpg h c G L (#i) T → 
              ⬆*[1] T ≡ U → cpg h c G (L.ⓑ{I}V) (#⫯i) U
 | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2.
              cpg h cV G L V1 V2 → cpg h cT G (L.ⓑ{I}V1) T1 T2 →
@@ -70,8 +70,8 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀J. T1 = ⓪{J} →
-                        ∨∨ T2 = ⓪{J}
-                         | ∃∃s. J = Sort s & T2 = ⋆(next h s)
+                        ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 
+                         | ∃∃s. J = Sort s & T2 = ⋆(next h s) & c = 𝟘𝟙
                          | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                          L = K.ⓓV1 & J = LRef 0 & c = ↓cV
                          | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
@@ -79,8 +79,8 @@ fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀
                          | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ➡[c, h] T & ⬆*[1] T ≡ T2 &
                                         L = K.ⓑ{I}V & J = LRef (⫯i).
 #c #h #G #L #T1 #T2 * -c -G -L -T1 -T2
-[ #I #G #L #J #H destruct /2 width=1 by or5_intro0/
-| #G #L #s #J #H destruct /3 width=3 by or5_intro1, ex2_intro/
+[ #I #G #L #J #H destruct /3 width=1 by or5_intro0, conj/
+| #G #L #s #J #H destruct /3 width=3 by or5_intro1, ex3_intro/
 | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro2, ex5_4_intro/
 | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro3, ex5_4_intro/
 | #c #I #G #L #V #T #U #i #HT #HTU #J #H destruct /3 width=9 by or5_intro4, ex4_5_intro/
@@ -95,8 +95,8 @@ fact cpg_inv_atom1_aux: ∀c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2 → ∀
 qed-.
 
 lemma cpg_inv_atom1: ∀c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[c, h] T2 →
-                     ∨∨ T2 = ⓪{J}
-                      | ∃∃s. J = Sort s & T2 = ⋆(next h s)
+                     ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 
+                      | ∃∃s. J = Sort s & T2 = ⋆(next h s) & c = 𝟘𝟙
                       | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                       L = K.ⓓV1 & J = LRef 0 & c = ↓cV
                       | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
@@ -106,23 +106,23 @@ lemma cpg_inv_atom1: ∀c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[c, h] T2 →
 /2 width=3 by cpg_inv_atom1_aux/ qed-.
 
 lemma cpg_inv_sort1: ∀c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ➡[c, h] T2 →
-                     T2 = ⋆s ∨ T2 = ⋆(next h s).
+                     (T2 = ⋆s ∧ c = 𝟘𝟘) ∨ (T2 = ⋆(next h s) ∧ c = 𝟘𝟙).
 #c #h #G #L #T2 #s #H
-elim (cpg_inv_atom1 … H) -H /2 width=1 by or_introl/ *
-[ #s0 #H destruct /2 width=1 by or_intror/
+elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/
+[ #s0 #H destruct /3 width=1 by or_intror, conj/
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
 | #I #K #V1 #V2 #i #_ #_ #_ #H destruct
 ]
 qed-.
 
 lemma cpg_inv_zero1: ∀c,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[c, h] T2 →
-                     ∨∨ T2 = #0 
+                     ∨∨ (T2 = #0 ∧ c = 𝟘𝟘)
                       | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                       L = K.ⓓV1 & c = ↓cV
                       | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                       L = K.ⓛV1 & c = (↓cV)+𝟘𝟙.
 #c #h #G #L #T2 #H
-elim (cpg_inv_atom1 … H) -H /2 width=1 by or3_intro0/ *
+elim (cpg_inv_atom1 … H) -H * /3 width=1 by or3_intro0, conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #HV12 #HVT2 #H1 #_ #H2 destruct /3 width=8 by or3_intro1, or3_intro2, ex4_4_intro/
 | #I #K #V1 #V2 #i #_ #_ #_ #H destruct
@@ -130,19 +130,19 @@ elim (cpg_inv_atom1 … H) -H /2 width=1 by or3_intro0/ *
 qed-.
 
 lemma cpg_inv_lref1: ∀c,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[c, h] T2 →
-                     (T2 = #⫯i) ∨
+                     (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨
                      ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ➡[c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V.
 #c #h #G #L #T2 #i #H
-elim (cpg_inv_atom1 … H) -H /2 width=1 by or_introl/ *
+elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
 | #I #K #V1 #V2 #j #HV2 #HVT2 #H1 #H2 destruct /3 width=7 by ex3_4_intro, or_intror/
 ]
 qed-.
 
-lemma cpg_inv_gref1: ∀c,h,G,L,T2,l.  ⦃G, L⦄ ⊢ §l ➡[c, h] T2 → T2 = §l.
+lemma cpg_inv_gref1: ∀c,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[c, h] T2 → T2 = §l ∧ c = 𝟘𝟘.
 #c #h #G #L #T2 #l #H
-elim (cpg_inv_atom1 … H) -H // *
+elim (cpg_inv_atom1 … H) -H * /2 width=1 by conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
 | #I #K #V1 #V2 #i #_ #_ #_ #H destruct
@@ -190,9 +190,9 @@ lemma cpg_inv_abbr1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ➡[c, h]
 /3 width=8 by ex4_4_intro, ex4_2_intro, or_introl, or_intror/
 qed-.
 
-lemma cpg_inv_abst1: ∀c,h,p,G,L,V1,T1,U2.  ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[c, h] U2 →
+lemma cpg_inv_abst1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[c, h] U2 →
                      ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ➡[cV, h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ➡[cT, h] T2 &
-                                    U2 = ⓛ{p} V2. T2 & c = (↓cV)+cT.
+                                    U2 = ⓛ{p}V2.T2 & c = (↓cV)+cT.
 #c #h #p #G #L #V1 #T1 #U2 #H elim (cpg_inv_bind1 … H) -H * 
 [ /3 width=8 by ex4_4_intro/
 | #c #T #_ #_ #_ #H destruct