partial commit: just the components before "static" ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
index d34212910fb438f2670efe003606b90699f1abd8..5475207142a1899fafe453795c184bed6d2ed43c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
@@ -25,50 +25,50 @@ interpretation "extended parallel reduction (local environment, sn variant)"
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lpx_inv_atom1: ∀h,g,L2. ⦃h, ⋆⦄ ⊢ ➡[g] L2 → L2 = ⋆.
+lemma lpx_inv_atom1: ∀h,g,L2. ⦃h, ⋆⦄ ⊢ ➡[h, g] L2 → L2 = ⋆.
 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
 
-lemma lpx_inv_pair1: ∀h,g,I,K1,V1,L2. ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[g] L2 →
-                     ∃∃K2,V2. ⦃h, K1⦄ ⊢ ➡[g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[g] V2 &
+lemma lpx_inv_pair1: ∀h,g,I,K1,V1,L2. ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] L2 →
+                     ∃∃K2,V2. ⦃h, K1⦄ ⊢ ➡[h, g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[h, g] V2 &
                              L2 = K2. ⓑ{I} V2.
 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
 
-lemma lpx_inv_atom2: ∀h,g,L1.  ⦃h, L1⦄ ⊢ ➡[g] ⋆ → L1 = ⋆.
+lemma lpx_inv_atom2: ∀h,g,L1.  ⦃h, L1⦄ ⊢ ➡[h, g] ⋆ → L1 = ⋆.
 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
 
-lemma lpx_inv_pair2: ∀h,g,I,L1,K2,V2.  ⦃h, L1⦄ ⊢ ➡[g] K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃h, K1⦄ ⊢ ➡[g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[g] V2 &
+lemma lpx_inv_pair2: ∀h,g,I,L1,K2,V2.  ⦃h, L1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2 →
+                     ∃∃K1,V1. ⦃h, K1⦄ ⊢ ➡[h, g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[h, g] V2 &
                              L1 = K1. ⓑ{I} V1.
 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lpx_refl: ∀h,g,L.  ⦃h, L⦄ ⊢ ➡[g] L.
+lemma lpx_refl: ∀h,g,L.  ⦃G, L⦄ ⊢ ➡[h, g] L.
 /2 width=1 by lpx_sn_refl/ qed.
 
-lemma lpx_pair: ∀h,g,I,K1,K2,V1,V2. ⦃h, K1⦄ ⊢ ➡[g] K2 → ⦃h, K1⦄ ⊢ V1 ➡[g] V2 →
-                ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[g] K2.ⓑ{I}V2.
+lemma lpx_pair: ∀h,g,I,K1,K2,V1,V2. ⦃h, K1⦄ ⊢ ➡[h, g] K2 → ⦃h, K1⦄ ⊢ V1 ➡[h, g] V2 →
+                ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2.
 /2 width=1/ qed.
 
-lemma lpx_append: ∀h,g,K1,K2. ⦃h, K1⦄ ⊢ ➡[g] K2 → ∀L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 →
-                  ⦃h, L1 @@ K1⦄ ⊢ ➡[g] L2 @@ K2.
+lemma lpx_append: ∀h,g,K1,K2. ⦃h, K1⦄ ⊢ ➡[h, g] K2 → ∀L1,L2. ⦃h, L1⦄ ⊢ ➡[h, g] L2 →
+                  ⦃h, L1 @@ K1⦄ ⊢ ➡[h, g] L2 @@ K2.
 /3 width=1 by lpx_sn_append, cpx_append/ qed.
 
-lemma lpr_lpx: ∀h,g,L1,L2. L1 ⊢ ➡ L2 → ⦃h, L1⦄ ⊢ ➡[g] L2.
+lemma lpr_lpx: ∀h,g,L1,L2. L1 ⊢ ➡ L2 → ⦃h, L1⦄ ⊢ ➡[h, g] L2.
 #h #g #L1 #L2 #H elim H -L1 -L2 // /3 width=1/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpx_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → |L1| = |L2|.
+lemma lpx_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[h, g] L2 → |L1| = |L2|.
 /2 width=2 by lpx_sn_fwd_length/ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma lpx_fwd_append1: ∀h,g,K1,L1,L. ⦃h, K1 @@ L1⦄ ⊢ ➡[g] L →
-                       ∃∃K2,L2. ⦃h, K1⦄ ⊢ ➡[g] K2 & L = K2 @@ L2.
+lemma lpx_fwd_append1: ∀h,g,K1,L1,L. ⦃h, K1 @@ L1⦄ ⊢ ➡[h, g] L →
+                       ∃∃K2,L2. ⦃h, K1⦄ ⊢ ➡[h, g] K2 & L = K2 @@ L2.
 /2 width=2 by lpx_sn_fwd_append1/ qed-.
 
-lemma lpx_fwd_append2: ∀h,g,L,K2,L2. ⦃h, L⦄ ⊢ ➡[g] K2 @@ L2 →
-                       ∃∃K1,L1. ⦃h, K1⦄ ⊢ ➡[g] K2 & L = K1 @@ L1.
+lemma lpx_fwd_append2: ∀h,g,L,K2,L2. ⦃G, L⦄ ⊢ ➡[h, g] K2 @@ L2 →
+                       ∃∃K1,L1. ⦃h, K1⦄ ⊢ ➡[h, g] K2 & L = K1 @@ L1.
 /2 width=2 by lpx_sn_fwd_append2/ qed-.