some restyling ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
index f69cb5e673d3ffdbf7f325f179ff30f0dd963c49..f47d6640e7641206ded87e8082f3599e238d2329 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
@@ -27,8 +27,8 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma lpr_bind (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ➡[h] K2 →
-                        ∀I1,I2. ⦃G, K1⦄ ⊢ I1 ➡[h] I2 → ⦃G, K1.ⓘ{I1}⦄ ⊢ ➡[h] K2.ⓘ{I2}.
+lemma lpr_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.
 
 (* Note: lemma 250 *)
@@ -37,60 +37,60 @@ lemma lpr_refl (h) (G): reflexive … (lpr h G).
 
 (* Advanced properties ******************************************************)
 
-lemma lpr_bind_refl_dx (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ➡[h] K2 →
-                                ∀I. ⦃G, K1.ⓘ{I}⦄ ⊢ ➡[h] K2.ⓘ{I}.
+lemma lpr_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 lpr_pair (h) (G): ∀K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h] V2 →
-                        ∀I. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h] K2.ⓑ{I}V2.
+lemma lpr_pair (h) (G): ∀K1,K2,V1,V2. ⦃G,K1⦄ ⊢ ➡[h] K2 → ⦃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: lpr_inv_atom1 *)
 (* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ➡[h] L2 → L2 = ⋆.
+lemma lpr_inv_atom_sn (h) (G): ∀L2. ⦃G,⋆⦄ ⊢ ➡[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
-lemma lpr_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 lpr_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: lpr_inv_atom2 *)
-lemma lpr_inv_atom_dx (h) (G): ∀L1. ⦃G, L1⦄ ⊢ ➡[h] ⋆ → L1 = ⋆.
+lemma lpr_inv_atom_dx (h) (G): ∀L1. ⦃G,L1⦄ ⊢ ➡[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
-lemma lpr_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 lpr_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 lpr_inv_unit_sn (h) (G): ∀I,L2,K1. ⦃G, K1.ⓤ{I}⦄ ⊢ ➡[h] L2 →
-                               ∃∃K2. ⦃G, K1⦄ ⊢ ➡[h] K2 & L2 = K2.ⓤ{I}.
+lemma lpr_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: lpr_inv_pair1 *)
 (* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_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 lpr_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 lpr_inv_unit_dx (h) (G): ∀I,L1,K2. ⦃G, L1⦄ ⊢ ➡[h] K2.ⓤ{I} →
-                               ∃∃K1. ⦃G, K1⦄ ⊢ ➡[h] K2 & L1 = K1.ⓤ{I}.
+lemma lpr_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: lpr_inv_pair2 *)
-lemma lpr_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 lpr_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 lpr_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 lpr_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-.
 
 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back