some restyling ...

[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 ae782872ca431f30b3d9f09ecd363a76274d45bf..14d34b21a87bede5bed3119697c4a13d8d6ef545 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
@@ -27,8 +27,8 @@ interpretation
 
 (* 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).
@@ -36,56 +36,56 @@ lemma lpx_refl (h) (G): reflexive … (lpx h G).
 
 (* 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): ∀K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 → ∀V1,V2. ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 →
-                        ∀I.⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2.
+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) (G): ∀I1,L2,K1. ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] L2 →
-                               ∃∃I2,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] 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) (G): ∀I2,L1,K2. ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓘ{I2} →
-                               ∃∃I1,K1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
+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}.
+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) (G): ∀I,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] L2 →
-                               ∃∃K2,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] 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}.
+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) (G): ∀I,L1,K2,V2. ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
-                               ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
+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) (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.
+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-.