syntactic components detached from basic_2 become static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
index 96305c55b0b2dfd1fbf181dd8cacb664fbfa8311..ae782872ca431f30b3d9f09ecd363a76274d45bf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
@@ -13,71 +13,79 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/predtysn_4.ma".
-include "basic_2/relocation/lex.ma".
+include "static_2/relocation/lex.ma".
 include "basic_2/rt_transition/cpx_ext.ma".
 
-(* UNBOUND PARALLEL RT-TRANSITION FOR LOCAL ENVIRONMENTS ********************)
+(* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
 
-definition lpx: sh → genv → relation lenv ≝
-                λh,G. lex (cpx h G).
+definition lpx (h) (G): relation lenv ≝
+                        lex (cpx h G).
 
 interpretation
-   "unbound parallel rt-transition (local environment)"
+   "unbound parallel rt-transition on all entries (local environment)"
    'PRedTySn h G L1 L2 = (lpx h G L1 L2).
 
 (* Basic properties *********************************************************)
 
-lemma lpx_bind: ∀h,G,K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
-                ∀I1,I2. ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 → ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] K2.ⓘ{I2}.
+lemma lpx_bind (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
+                        ∀I1,I2. ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 → ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] K2.ⓘ{I2}.
 /2 width=1 by lex_bind/ qed.
 
-lemma lpx_refl: ∀h,G. reflexive … (lpx h G).
+lemma lpx_refl (h) (G): reflexive … (lpx h G).
 /2 width=1 by lex_refl/ qed.
 
 (* Advanced properties ******************************************************)
 
-lemma lpx_bind_refl_dx: ∀h,G,K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
-                        ∀I. ⦃G, K1.ⓘ{I}⦄ ⊢ ⬈[h] K2.ⓘ{I}.
+lemma lpx_bind_refl_dx (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
+                                ∀I. ⦃G, K1.ⓘ{I}⦄ ⊢ ⬈[h] K2.ⓘ{I}.
 /2 width=1 by lex_bind_refl_dx/ qed.
-(*
-lemma lpx_pair: ∀h,g,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 → ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 →
-                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2.
-/2 width=1 by lpx_sn_pair/ qed.
-*)
+
+lemma lpx_pair (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 → ∀V1,V2. ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 →
+                        ∀I.⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2.
+/2 width=1 by lex_pair/ qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpx_inv_atom1 *)
-lemma lpx_inv_atom_sn: ∀h,G,L2. ⦃G, ⋆⦄ ⊢ ⬈[h] L2 → L2 = ⋆.
+lemma lpx_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ⬈[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
-lemma lpx_inv_bind_sn: ∀h,I1,G,L2,K1. ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] L2 →
-                       ∃∃I2,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
-                                L2 = K2.ⓘ{I2}.
+lemma lpx_inv_bind_sn (h) (G): ∀I1,L2,K1. ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] L2 →
+                               ∃∃I2,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
+                                        L2 = K2.ⓘ{I2}.
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpx_inv_atom2 *)
-lemma lpx_inv_atom_dx: ∀h,G,L1.  ⦃G, L1⦄ ⊢ ⬈[h] ⋆ → L1 = ⋆.
+lemma lpx_inv_atom_dx: ∀h,G,L1. ⦃G, L1⦄ ⊢ ⬈[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
-lemma lpx_inv_bind_dx: ∀h,I2,G,L1,K2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓘ{I2} →
-                       ∃∃I1,K1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
-                                L1 = K1.ⓘ{I1}.
+lemma lpx_inv_bind_dx (h) (G): ∀I2,L1,K2. ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓘ{I2} →
+                               ∃∃I1,K1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
+                                        L1 = K1.ⓘ{I1}.
 /2 width=1 by lex_inv_bind_dx/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
+lemma lpx_inv_unit_sn (h) (G): ∀I,L2,K1. ⦃G, K1.ⓤ{I}⦄ ⊢ ⬈[h] L2 →
+                               ∃∃K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & L2 = K2.ⓤ{I}.
+/2 width=1 by lex_inv_unit_sn/ qed-.
+
 (* Basic_2A1: was: lpx_inv_pair1 *)
-lemma lpx_inv_pair_sn: ∀h,I,G,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] L2 →
-                       ∃∃K2,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
-                                L2 = K2.ⓑ{I}V2.
+lemma lpx_inv_pair_sn (h) (G): ∀I,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] L2 →
+                               ∃∃K2,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
+                                        L2 = K2.ⓑ{I}V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
+lemma lpx_inv_unit_dx (h) (G): ∀I,L1,K2. ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓤ{I} →
+                               ∃∃K1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & L1 = K1.ⓤ{I}.
+/2 width=1 by lex_inv_unit_dx/ qed-.
+
 (* Basic_2A1: was: lpx_inv_pair2 *)
-lemma lpx_inv_pair_dx: ∀h,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
-                       ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
-                                L1 = K1.ⓑ{I}V1.
+lemma lpx_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
+                               ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
+                                        L1 = K1.ⓑ{I}V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
-lemma lpx_inv_pair: ∀h,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ⬈[h] L2.ⓑ{I2}V2 →
-                    ∧∧ ⦃G, L1⦄ ⊢ ⬈[h] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 & I1 = I2.
+lemma lpx_inv_pair (h) (G): ∀I1,I2,L1,L2,V1,V2. ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ⬈[h] L2.ⓑ{I2}V2 →
+                            ∧∧ ⦃G, L1⦄ ⊢ ⬈[h] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 & I1 = I2.
 /2 width=1 by lex_inv_pair/ qed-.