made executable again

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
index 172421887eb459899d8b83bbce1bc383b796237d..66d0bc288520ce564f774d918ea539d9185057f2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
@@ -25,24 +25,24 @@ include "basic_2/rt_transition/cpm.ma".
 (* Note: cpr_flat: does not hold in basic_1 *)
 (* Basic_1: includes: pr2_thin_dx *)
 lemma cpr_flat: ∀h,I,G,L,V1,V2,T1,T2.
-                â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,0] T2 →
-                â\9dªG,Lâ\9d« ⊢ ⓕ[I]V1.T1 ➡[h,0] ⓕ[I]V2.T2.
+                â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,0] T2 →
+                â\9d¨G,Lâ\9d© ⊢ ⓕ[I]V1.T1 ➡[h,0] ⓕ[I]V2.T2.
 #h * /2 width=1 by cpm_cast, cpm_appl/
 qed.
 
 (* Basic_1: was: pr2_head_1 *)
-lemma cpr_pair_sn: â\88\80h,I,G,L,V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V2 →
-                   â\88\80T. â\9dªG,Lâ\9d« ⊢ ②[I]V1.T ➡[h,0] ②[I]V2.T.
+lemma cpr_pair_sn: â\88\80h,I,G,L,V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V2 →
+                   â\88\80T. â\9d¨G,Lâ\9d© ⊢ ②[I]V1.T ➡[h,0] ②[I]V2.T.
 #h * /2 width=1 by cpm_bind, cpr_flat/
 qed.
 
 (* Basic inversion properties ***********************************************)
 
-lemma cpr_inv_atom1: â\88\80h,J,G,L,T2. â\9dªG,Lâ\9d« ⊢ ⓪[J] ➡[h,0] T2 →
+lemma cpr_inv_atom1: â\88\80h,J,G,L,T2. â\9d¨G,Lâ\9d© ⊢ ⓪[J] ➡[h,0] T2 →
                      ∨∨ T2 = ⓪[J]
-                      | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,0] V2 & ⇧[1] V2 ≘ T2 &
+                      | â\88\83â\88\83K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,0] V2 & ⇧[1] V2 ≘ T2 &
                                    L = K.ⓓV1 & J = LRef 0
-                      | â\88\83â\88\83I,K,T,i. â\9dªG,Kâ\9d« ⊢ #i ➡[h,0] T & ⇧[1] T ≘ T2 &
+                      | â\88\83â\88\83I,K,T,i. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,0] T & ⇧[1] T ≘ T2 &
                                    L = K.ⓘ[I] & J = LRef (↑i).
 #h #J #G #L #T2 #H elim (cpm_inv_atom1 … H) -H *
 [2,4:|*: /3 width=8 by or3_intro0, or3_intro1, or3_intro2, ex4_4_intro, ex4_3_intro/ ]
@@ -52,48 +52,48 @@ lemma cpr_inv_atom1: ∀h,J,G,L,T2. ❪G,L❫ ⊢ ⓪[J] ➡[h,0] T2 →
 qed-.
 
 (* Basic_1: includes: pr0_gen_sort pr2_gen_sort *)
-lemma cpr_inv_sort1: â\88\80h,G,L,T2,s. â\9dªG,Lâ\9d« ⊢ ⋆s ➡[h,0] T2 → T2 = ⋆s.
+lemma cpr_inv_sort1: â\88\80h,G,L,T2,s. â\9d¨G,Lâ\9d© ⊢ ⋆s ➡[h,0] T2 → T2 = ⋆s.
 #h #G #L #T2 #s #H elim (cpm_inv_sort1 … H) -H //
 qed-.
 
-lemma cpr_inv_zero1: â\88\80h,G,L,T2. â\9dªG,Lâ\9d« ⊢ #0 ➡[h,0] T2 →
+lemma cpr_inv_zero1: â\88\80h,G,L,T2. â\9d¨G,Lâ\9d© ⊢ #0 ➡[h,0] T2 →
                      ∨∨ T2 = #0
-                      | â\88\83â\88\83K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,0] V2 & ⇧[1] V2 ≘ T2 &
+                      | â\88\83â\88\83K,V1,V2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,0] 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: â\88\80h,G,L,T2,i. â\9dªG,Lâ\9d« ⊢ #↑i ➡[h,0] T2 →
+lemma cpr_inv_lref1: â\88\80h,G,L,T2,i. â\9d¨G,Lâ\9d© ⊢ #↑i ➡[h,0] T2 →
                      ∨∨ T2 = #(↑i)
-                      | â\88\83â\88\83I,K,T. â\9dªG,Kâ\9d« ⊢ #i ➡[h,0] T & ⇧[1] T ≘ T2 & L = K.ⓘ[I].
+                      | â\88\83â\88\83I,K,T. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,0] T & ⇧[1] T ≘ 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-.
 
-lemma cpr_inv_gref1: â\88\80h,G,L,T2,l. â\9dªG,Lâ\9d« ⊢ §l ➡[h,0] T2 → T2 = §l.
+lemma cpr_inv_gref1: â\88\80h,G,L,T2,l. â\9d¨G,Lâ\9d© ⊢ §l ➡[h,0] T2 → T2 = §l.
 #h #G #L #T2 #l #H elim (cpm_inv_gref1 … H) -H //
 qed-.
 
 (* Basic_1: includes: pr0_gen_cast pr2_gen_cast *)
-lemma cpr_inv_cast1: â\88\80h,G,L,V1,U1,U2. â\9dªG,Lâ\9d« ⊢ ⓝ V1.U1 ➡[h,0] U2 →
-                     â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,Lâ\9d« ⊢ U1 ➡[h,0] T2 &
+lemma cpr_inv_cast1: â\88\80h,G,L,V1,U1,U2. â\9d¨G,Lâ\9d© ⊢ ⓝ V1.U1 ➡[h,0] U2 →
+                     â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,0] T2 &
                                  U2 = ⓝV2.T2
-                      | â\9dªG,Lâ\9d« ⊢ U1 ➡[h,0] U2.
+                      | â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,0] 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-.
 
-lemma cpr_inv_flat1: â\88\80h,I,G,L,V1,U1,U2. â\9dªG,Lâ\9d« ⊢ ⓕ[I]V1.U1 ➡[h,0] U2 →
-                     â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,Lâ\9d« ⊢ U1 ➡[h,0] T2 &
+lemma cpr_inv_flat1: â\88\80h,I,G,L,V1,U1,U2. â\9d¨G,Lâ\9d© ⊢ ⓕ[I]V1.U1 ➡[h,0] U2 →
+                     â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,0] T2 &
                                  U2 = ⓕ[I]V2.T2
-                      | (â\9dªG,Lâ\9d« ⊢ U1 ➡[h,0] U2 ∧ I = Cast)
-                      | â\88\83â\88\83p,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 & â\9dªG,Lâ\9d« ⊢ W1 ➡[h,0] W2 &
-                                            â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡[h,0] T2 & U1 = ⓛ[p]W1.T1 &
+                      | (â\9d¨G,Lâ\9d© ⊢ U1 ➡[h,0] U2 ∧ I = Cast)
+                      | â\88\83â\88\83p,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 & â\9d¨G,Lâ\9d© ⊢ W1 ➡[h,0] W2 &
+                                            â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡[h,0] T2 & U1 = ⓛ[p]W1.T1 &
                                             U2 = ⓓ[p]ⓝW2.V2.T2 & I = Appl
-                      | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V & ⇧[1] V ≘ V2 &
-                                              â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 & â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡[h,0] T2 &
+                      | â\88\83â\88\83p,V,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V & ⇧[1] V ≘ V2 &
+                                              â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 & â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡[h,0] T2 &
                                               U1 = ⓓ[p]W1.T1 &
                                               U2 = ⓓ[p]W2.ⓐV2.T2 & I = Appl.
 #h * #G #L #V1 #U1 #U2 #H
@@ -108,26 +108,26 @@ qed-.
 
 lemma cpr_ind (h): ∀Q:relation4 genv lenv term term.
                    (∀I,G,L. Q G L (⓪[I]) (⓪[I])) →
-                   (â\88\80G,K,V1,V2,W2. â\9dªG,Kâ\9d« ⊢ V1 ➡[h,0] V2 → Q G K V1 V2 →
+                   (â\88\80G,K,V1,V2,W2. â\9d¨G,Kâ\9d© ⊢ V1 ➡[h,0] V2 → Q G K V1 V2 →
                      ⇧[1] V2 ≘ W2 → Q G (K.ⓓV1) (#0) W2
-                   ) â\86\92 (â\88\80I,G,K,T,U,i. â\9dªG,Kâ\9d« ⊢ #i ➡[h,0] T → Q G K (#i) T →
+                   ) â\86\92 (â\88\80I,G,K,T,U,i. â\9d¨G,Kâ\9d© ⊢ #i ➡[h,0] T → Q G K (#i) T →
                      ⇧[1] T ≘ U → Q G (K.ⓘ[I]) (#↑i) (U)
-                   ) â\86\92 (â\88\80p,I,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡[h,0] T2 →
+                   ) â\86\92 (â\88\80p,I,G,L,V1,V2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ➡[h,0] T2 →
                      Q G L V1 V2 → Q G (L.ⓑ[I]V1) T1 T2 → Q G L (ⓑ[p,I]V1.T1) (ⓑ[p,I]V2.T2)
-                   ) â\86\92 (â\88\80I,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡[h,0] T2 →
+                   ) â\86\92 (â\88\80I,G,L,V1,V2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,0] 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\87§[1] T â\89\98 T1 â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡[h,0] T2 →
+                   ) â\86\92 (â\88\80G,L,V,T1,T,T2. â\87§[1] T â\89\98 T1 â\86\92 â\9d¨G,Lâ\9d© ⊢ T ➡[h,0] T2 →
                      Q G L T T2 → Q G L (+ⓓV.T1) T2
-                   ) â\86\92 (â\88\80G,L,V,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,0] T2 → Q G L T1 T2 →
+                   ) â\86\92 (â\88\80G,L,V,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,0] T2 → Q G L T1 T2 →
                      Q G L (ⓝV.T1) T2
-                   ) â\86\92 (â\88\80p,G,L,V1,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡[h,0] T2 →
+                   ) â\86\92 (â\88\80p,G,L,V1,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V2 â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡[h,0] T2 →
                      Q G L V1 V2 → Q G L W1 W2 → Q G (L.ⓛW1) T1 T2 →
                      Q G L (ⓐV1.ⓛ[p]W1.T1) (ⓓ[p]ⓝW2.V2.T2)
-                   ) â\86\92 (â\88\80p,G,L,V1,V,V2,W1,W2,T1,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡[h,0] T2 →
+                   ) â\86\92 (â\88\80p,G,L,V1,V,V2,W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡[h,0] V â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â\9e¡[h,0] W2 â\86\92 â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡[h,0] T2 →
                      Q G L V1 V → Q G L W1 W2 → Q G (L.ⓓW1) T1 T2 →
                      ⇧[1] V ≘ V2 → Q G L (ⓐV1.ⓓ[p]W1.T1) (ⓓ[p]W2.ⓐV2.T2)
                    ) →
-                   â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[h,0] T2 → Q G L T1 T2.
+                   â\88\80G,L,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡[h,0] T2 → Q G L T1 T2.
 #h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #G #L #T1 #T2
 @(insert_eq_0 … 0) #n #H
 @(cpm_ind … H) -G -L -T1 -T2 -n [2,4,11:|*: /3 width=4 by/ ]