notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx.ma
index 9fd1ccf480bbda238bed577bf1db8904076ee76b..dd8fcdb85b66f3272949b4aaf8f931014cc0590a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx.ma
@@ -21,10 +21,10 @@ include "basic_2/reduction/cpr.ma".
 (* avtivate genv *)
 inductive cpx (h) (g): relation4 genv lenv term term ≝
 | cpx_atom : ∀I,G,L. cpx h g G L (⓪{I}) (⓪{I})
-| cpx_sort : ∀G,L,k,l. deg h g k (l+1) → cpx h g G L (⋆k) (⋆(next h k))
+| cpx_st   : ∀G,L,k,l. deg h g k (l+1) → cpx h g G L (⋆k) (⋆(next h k))
 | cpx_delta: ∀I,G,L,K,V,V2,W2,i.
-             â\87©[i] L ≡ K.ⓑ{I}V → cpx h g G K V V2 →
-             â\87§[0, i+1] V2 ≡ W2 → cpx h g G L (#i) W2
+             â¬\87[i] L ≡ K.ⓑ{I}V → cpx h g G K V V2 →
+             â¬\86[0, i+1] V2 ≡ W2 → cpx h g G L (#i) W2
 | cpx_bind : ∀a,I,G,L,V1,V2,T1,T2.
              cpx h g G L V1 V2 → cpx h g G (L.ⓑ{I}V1) T1 T2 →
              cpx h g G L (ⓑ{a,I}V1.T1) (ⓑ{a,I}V2.T2)
@@ -32,14 +32,14 @@ inductive cpx (h) (g): relation4 genv lenv term term ≝
              cpx h g G L V1 V2 → cpx h g G L T1 T2 →
              cpx h g G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
 | cpx_zeta : ∀G,L,V,T1,T,T2. cpx h g G (L.ⓓV) T1 T →
-             â\87§[0, 1] T2 ≡ T → cpx h g G L (+ⓓV.T1) T2
-| cpx_tau  : ∀G,L,V,T1,T2. cpx h g G L T1 T2 → cpx h g G L (ⓝV.T1) T2
-| cpx_ti   : ∀G,L,V1,V2,T. cpx h g G L V1 V2 → cpx h g G L (ⓝV1.T) V2
+             â¬\86[0, 1] T2 ≡ T → cpx h g G L (+ⓓV.T1) T2
+| cpx_eps  : ∀G,L,V,T1,T2. cpx h g G L T1 T2 → cpx h g G L (ⓝV.T1) T2
+| cpx_ct   : ∀G,L,V1,V2,T. cpx h g G L V1 V2 → cpx h g G L (ⓝV1.T) V2
 | cpx_beta : ∀a,G,L,V1,V2,W1,W2,T1,T2.
              cpx h g G L V1 V2 → cpx h g G L W1 W2 → cpx h g G (L.ⓛW1) T1 T2 →
              cpx h g G L (ⓐV1.ⓛ{a}W1.T1) (ⓓ{a}ⓝW2.V2.T2)
 | cpx_theta: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
-             cpx h g G L V1 V â\86\92 â\87§[0, 1] V ≡ V2 → cpx h g G L W1 W2 →
+             cpx h g G L V1 V â\86\92 â¬\86[0, 1] V ≡ V2 → cpx h g G L W1 W2 →
              cpx h g G (L.ⓓW1) T1 T2 →
              cpx h g G L (ⓐV1.ⓓ{a}W1.T1) (ⓓ{a}W2.ⓐV2.T2)
 .
@@ -53,13 +53,13 @@ interpretation
 lemma lsubr_cpx_trans: ∀h,g,G. lsub_trans … (cpx h g G) lsubr.
 #h #g #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
 [ //
-| /2 width=2 by cpx_sort/
+| /2 width=2 by cpx_st/
 | #I #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
-  elim (lsubr_fwd_ldrop2_bind … HL12 … HLK1) -HL12 -HLK1 *
-  /4 width=7 by cpx_delta, cpx_ti/
-|4,9: /4 width=1 by cpx_bind, cpx_beta, lsubr_bind/
-|5,7,8: /3 width=1 by cpx_flat, cpx_tau, cpx_ti/
-|6,10: /4 width=3 by cpx_zeta, cpx_theta, lsubr_bind/
+  elim (lsubr_fwd_drop2_pair … HL12 … HLK1) -HL12 -HLK1 *
+  /4 width=7 by cpx_delta, cpx_ct/
+|4,9: /4 width=1 by cpx_bind, cpx_beta, lsubr_pair/
+|5,7,8: /3 width=1 by cpx_flat, cpx_eps, cpx_ct/
+|6,10: /4 width=3 by cpx_zeta, cpx_theta, lsubr_pair/
 ]
 qed-.
 
@@ -70,7 +70,7 @@ qed.
 
 lemma cpr_cpx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
 #h #g #G #L #T1 #T2 #H elim H -L -T1 -T2
-/2 width=7 by cpx_delta, cpx_bind, cpx_flat, cpx_zeta, cpx_tau, cpx_beta, cpx_theta/
+/2 width=7 by cpx_delta, cpx_bind, cpx_flat, cpx_zeta, cpx_eps, cpx_beta, cpx_theta/
 qed.
 
 lemma cpx_pair_sn: ∀h,g,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
@@ -78,8 +78,8 @@ lemma cpx_pair_sn: ∀h,g,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 →
 #h #g * /2 width=1 by cpx_bind, cpx_flat/
 qed.
 
-lemma cpx_delift: â\88\80h,g,I,G,K,V,T1,L,d. â\87©[d] L ≡ (K.ⓑ{I}V) →
-                  â\88\83â\88\83T2,T.  â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h, g] T2 & â\87§[d, 1] T ≡ T2.
+lemma cpx_delift: â\88\80h,g,I,G,K,V,T1,L,d. â¬\87[d] L ≡ (K.ⓑ{I}V) →
+                  â\88\83â\88\83T2,T.  â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h, g] T2 & â¬\86[d, 1] T ≡ T2.
 #h #g #I #G #K #V #T1 elim T1 -T1
 [ * #i #L #d /2 width=4 by cpx_atom, lift_sort, lift_gref, ex2_2_intro/
   elim (lt_or_eq_or_gt i d) #Hid [1,3: /3 width=4 by cpx_atom, lift_lref_ge_minus, lift_lref_lt, ex2_2_intro/ ]
@@ -88,7 +88,7 @@ lemma cpx_delift: ∀h,g,I,G,K,V,T1,L,d. ⇩[d] L ≡ (K.ⓑ{I}V) →
   elim (lift_split … HVW i i) /3 width=7 by cpx_delta, ex2_2_intro/
 | * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #d #HLK
   elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2
-  [ elim (IHU1 (L. ⓑ{I} W1) (d+1)) -IHU1 /3 width=9 by cpx_bind, ldrop_drop, lift_bind, ex2_2_intro/
+  [ elim (IHU1 (L. ⓑ{I} W1) (d+1)) -IHU1 /3 width=9 by cpx_bind, drop_drop, lift_bind, ex2_2_intro/
   | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8 by cpx_flat, lift_flat, ex2_2_intro/
   ]
 ]
@@ -99,8 +99,8 @@ qed-.
 fact cpx_inv_atom1_aux: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → ∀J. T1 = ⓪{J} →
                         ∨∨ T2 = ⓪{J}
                          | ∃∃k,l. deg h g k (l+1) & T2 = ⋆(next h k) & J = Sort k
-                         | â\88\83â\88\83I,K,V,V2,i. â\87©[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
-                                         â\87§[O, i+1] V2 ≡ T2 & J = LRef i.
+                         | â\88\83â\88\83I,K,V,V2,i. â¬\87[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
+                                         â¬\86[O, i+1] V2 ≡ T2 & J = LRef i.
 #G #h #g #L #T1 #T2 * -L -T1 -T2
 [ #I #G #L #J #H destruct /2 width=1 by or3_intro0/
 | #G #L #k #l #Hkl #J #H destruct /3 width=5 by or3_intro1, ex3_2_intro/
@@ -118,8 +118,8 @@ qed-.
 lemma cpx_inv_atom1: ∀h,g,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[h, g] T2 →
                      ∨∨ T2 = ⓪{J}
                       | ∃∃k,l. deg h g k (l+1) & T2 = ⋆(next h k) & J = Sort k
-                      | â\88\83â\88\83I,K,V,V2,i. â\87©[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
-                                      â\87§[O, i+1] V2 ≡ T2 & J = LRef i.
+                      | â\88\83â\88\83I,K,V,V2,i. â¬\87[i] L ≡ K.ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
+                                      â¬\86[O, i+1] V2 ≡ T2 & J = LRef i.
 /2 width=3 by cpx_inv_atom1_aux/ qed-.
 
 lemma cpx_inv_sort1: ∀h,g,G,L,T2,k. ⦃G, L⦄ ⊢ ⋆k ➡[h, g] T2 → T2 = ⋆k ∨
@@ -133,8 +133,8 @@ qed-.
 
 lemma cpx_inv_lref1: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h, g] T2 →
                      T2 = #i ∨
-                     â\88\83â\88\83I,K,V,V2. â\87©[i] L ≡ K. ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
-                                 â\87§[O, i+1] V2 ≡ T2.
+                     â\88\83â\88\83I,K,V,V2. â¬\87[i] L ≡ K. ⓑ{I}V & ⦃G, K⦄ ⊢ V ➡[h, g] V2 &
+                                 â¬\86[O, i+1] V2 ≡ T2.
 #h #g #G #L #T2 #i #H
 elim (cpx_inv_atom1 … H) -H /2 width=1 by or_introl/ *
 [ #k #l #_ #_ #H destruct
@@ -144,7 +144,7 @@ qed-.
 
 lemma cpx_inv_lref1_ge: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h, g] T2 → |L| ≤ i → T2 = #i.
 #h #g #G #L #T2 #i #H elim (cpx_inv_lref1 … H) -H // *
-#I #K #V1 #V2 #HLK #_ #_ #HL -h -G -V2 lapply (ldrop_fwd_length_lt2 … HLK) -K -I -V1
+#I #K #V1 #V2 #HLK #_ #_ #HL -h -G -V2 lapply (drop_fwd_length_lt2 … HLK) -K -I -V1
 #H elim (lt_refl_false i) /2 width=3 by lt_to_le_to_lt/
 qed-.
 
@@ -161,7 +161,7 @@ fact cpx_inv_bind1_aux: ∀h,g,G,L,U1,U2. ⦃G, L⦄ ⊢ U1 ➡[h, g] U2 →
                         ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 & ⦃G, L.ⓑ{J}V1⦄ ⊢ T1 ➡[h, g] T2 &
                                  U2 = ⓑ{a,J}V2.T2
                         ) ∨
-                        â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â\87§[0, 1] U2 ≡ T &
+                        â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â¬\86[0, 1] U2 ≡ T &
                              a = true & J = Abbr.
 #h #g #G #L #U1 #U2 * -L -U1 -U2
 [ #I #G #L #b #J #W #U1 #H destruct
@@ -181,7 +181,7 @@ lemma cpx_inv_bind1: ∀h,g,a,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡[h
                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[h, g] T2 &
                               U2 = ⓑ{a,I} V2. T2
                      ) ∨
-                     â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â\87§[0, 1] U2 ≡ T &
+                     â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â¬\86[0, 1] U2 ≡ T &
                           a = true & I = Abbr.
 /2 width=3 by cpx_inv_bind1_aux/ qed-.
 
@@ -189,7 +189,7 @@ lemma cpx_inv_abbr1: ∀h,g,a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{a}V1.T1 ➡[h, g]
                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[h, g] T2 &
                               U2 = ⓓ{a} V2. T2
                      ) ∨
-                     â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â\87§[0, 1] U2 ≡ T & a = true.
+                     â\88\83â\88\83T. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡[h, g] T & â¬\86[0, 1] U2 ≡ T & a = true.
 #h #g #a #G #L #V1 #T1 #U2 #H
 elim (cpx_inv_bind1 … H) -H * /3 width=5 by ex3_2_intro, ex3_intro, or_introl, or_intror/
 qed-.
@@ -214,7 +214,7 @@ fact cpx_inv_flat1_aux: ∀h,g,G,L,U,U2. ⦃G, L⦄ ⊢ U ➡[h, g] U2 →
                                                ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h, g] T2 &
                                                U1 = ⓛ{a}W1.T1 &
                                                U2 = ⓓ{a}ⓝW2.V2.T2 & J = Appl
-                         | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â\87§[0,1] V ≡ V2 &
+                         | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â¬\86[0,1] V ≡ V2 &
                                                  ⦃G, L⦄ ⊢ W1 ➡[h, g] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h, g] T2 &
                                                  U1 = ⓓ{a}W1.T1 &
                                                  U2 = ⓓ{a}W2.ⓐV2.T2 & J = Appl.
@@ -241,7 +241,7 @@ lemma cpx_inv_flat1: ∀h,g,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ➡[h, g]
                                             ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h, g] T2 &
                                             U1 = ⓛ{a}W1.T1 &
                                             U2 = ⓓ{a}ⓝW2.V2.T2 & I = Appl
-                      | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â\87§[0,1] V ≡ V2 &
+                      | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â¬\86[0,1] V ≡ V2 &
                                               ⦃G, L⦄ ⊢ W1 ➡[h, g] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h, g] T2 &
                                               U1 = ⓓ{a}W1.T1 &
                                               U2 = ⓓ{a}W2.ⓐV2.T2 & I = Appl.
@@ -253,7 +253,7 @@ lemma cpx_inv_appl1: ∀h,g,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ➡[h, g] U2
                       | ∃∃a,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 & ⦃G, L⦄ ⊢ W1 ➡[h, g] W2 &
                                             ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h, g] T2 &
                                             U1 = ⓛ{a}W1.T1 & U2 = ⓓ{a}ⓝW2.V2.T2
-                      | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â\87§[0,1] V ≡ V2 &
+                      | â\88\83â\88\83a,V,V2,W1,W2,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡[h, g] V & â¬\86[0,1] V ≡ V2 &
                                               ⦃G, L⦄ ⊢ W1 ➡[h, g] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h, g] T2 &
                                               U1 = ⓓ{a}W1.T1 & U2 = ⓓ{a}W2. ⓐV2. T2.
 #h #g #G #L #V1 #U1 #U2 #H elim (cpx_inv_flat1 … H) -H *