milestone update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
index c06e0278d02249239453d0b543644278b47874c2..827a963be43836ab25f59e72b583677b5c80d0b6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
@@ -27,20 +27,53 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma lprs_refl (h) (G): ∀L. ⦃G, L⦄ ⊢ ➡*[h] L.
-/2 width=1 by lex_refl/ qed.
-
 (* Basic_2A1: uses: lprs_pair_refl *)
 lemma lprs_bind_refl_dx (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
                                  ∀I. ⦃G, L1.ⓘ{I}⦄ ⊢ ➡*[h] L2.ⓘ{I}.
 /2 width=1 by lex_bind_refl_dx/ qed.
 
+lemma lprs_pair (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
+                         ∀V1,V2. ⦃G, L1⦄ ⊢ V1 ➡*[h] V2 →
+                         ∀I. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡*[h] L2.ⓑ{I}V2.
+/2 width=1 by lex_pair/ qed.
+
+lemma lprs_refl (h) (G): ∀L. ⦃G, L⦄ ⊢ ➡*[h] L.
+/2 width=1 by lex_refl/ qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: lprs_inv_atom1 *)
 lemma lprs_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ➡*[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
+(* Basic_2A1: was: lprs_inv_pair1 *)
+lemma lprs_inv_pair_sn (h) (G):
+                       ∀I,K1,L2,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-.
+
 (* Basic_2A1: uses: lprs_inv_atom2 *)
 lemma lprs_inv_atom_dx (h) (G): ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
+
+(* Basic_2A1: was: lprs_inv_pair2 *)
+lemma lprs_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-.
+
+(* Basic eliminators ********************************************************)
+
+(* Basic_2A1: was: lprs_ind_alt *)
+lemma lprs_ind (h) (G): ∀R:relation lenv.
+                        R (⋆) (⋆) → (
+                          ∀I,K1,K2.
+                          ⦃G, K1⦄ ⊢ ➡*[h] K2 →
+                          R K1 K2 → R (K1.ⓘ{I}) (K2.ⓘ{I})
+                        ) → (
+                          ∀I,K1,K2,V1,V2.
+                          ⦃G, K1⦄ ⊢ ➡*[h] K2 → ⦃G, K1⦄ ⊢ V1 ➡*[h] V2 →
+                          R K1 K2 → R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
+                        ) →
+                        ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L1 L2.
+/3 width=4 by lex_ind/ qed-.