- exclusion binder added in local environments

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubf_lsubf.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_lsubf.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_lsubf.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_lsubf.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground_2/relocation/nstream_sor.ma".
+include "basic_2/static/frees_frees.ma".
+include "basic_2/static/lsubf.ma".
+
+(* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
+
+(* Main properties **********************************************************)
+
+theorem lsubf_sor: ∀K,L,g1,f1. ⦃K, g1⦄ ⫃𝐅* ⦃L, f1⦄ →
+                   ∀g2,f2. ⦃K, g2⦄ ⫃𝐅* ⦃L, f2⦄ →
+                   ∀g. g1 ⋓ g2 ≡ g → ∀f. f1 ⋓ f2 ≡ f → ⦃K, g⦄ ⫃𝐅* ⦃L, f⦄.
+#K elim K -K
+[ #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
+  elim (lsubf_inv_atom1 … H1) -H1 #H1 #H destruct
+  lapply (lsubf_inv_atom … H2) -H2 #H2
+  /5 width=4 by lsubf_atom, sor_mono, sor_eq_repl_back2, sor_eq_repl_back1/
+| #K #J #IH #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
+  elim (pn_split g1) * #y1 #H destruct
+  elim (pn_split g2) * #y2 #H destruct
+  [ elim (sor_inv_ppx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
+    elim (lsubf_inv_push_sn … H2) -H2 #x2 #H2 #H destruct
+    elim (sor_inv_ppx … Hf) -Hf [|*: // ] #x #Hx #H destruct
+    /3 width=8 by lsubf_push/
+  | elim (sor_inv_pnx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
+    generalize in match H2; -H2 cases J -J #J [| #V ] #H2
+    [ elim (lsubf_inv_unit1 … H2) -H2 #x2 #Y2 #H2 #H #H0 destruct
+    | elim (lsubf_inv_pair1 … H2) -H2 *
+      [ #x2 #Z2 #H2 #H #H0 destruct
+      | #y3 #y4 #x2 #Y2 #W #U #H2 #Hy3 #Hy2 #H #H0 #H3 #H4 destruct
+      | #y3 #y4 #x2 #Z2 #Y2 #H2 #Hy3 #Hy2 #H #H0 destruct
+      ]
+    ]
+    elim (sor_inv_pnx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_trans2/
+  | elim (sor_inv_npx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (lsubf_inv_push1 … H2) -H2 #x2 #Z2 #Y2 #H2 #H #H0 destruct
+    generalize in match H1; -H1 cases J -J #J [| #V ] #H1
+    [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
+    | elim (lsubf_inv_pair1 … H1) -H1 *
+      [ #x1 #Z1 #H1 #H #H0 destruct
+      | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
+      | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
+      ]
+    ]
+    elim (sor_inv_npx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_trans1_sym/
+  | elim (sor_inv_nnx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    generalize in match H2; generalize in match H1; -H1 -H2 cases J -J #J [| #V ] #H1 #H2
+    [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
+      elim (lsubf_inv_bind_sn … H2) -H2 #x2 #H2 #H destruct
+    | elim (lsubf_inv_pair1 … H1) -H1 *
+      [ #x1 #Z1 #H1 #H #H0 destruct
+        elim (lsubf_inv_bind_sn … H2) -H2 #x2 #H2 #H destruct
+      | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
+        elim (lsubf_inv_beta_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
+        lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
+        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+      | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
+        elim (lsubf_inv_unit_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
+        lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
+        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+      ]
+    ]
+    elim (sor_inv_nnx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_distr_dx/
+  ]
+]
+qed-.