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

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
index 4cf6a28b419414fb3f84b073eb57ee546b3b35e3..c2d0eb2cfee07866041b196fc3c638ce6936c73c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
@@ -26,48 +26,48 @@ interpretation "extended parallel computation (local environment, sn variant)"
 (* Basic eliminators ********************************************************)
 
 lemma lpxs_ind: ∀h,g,L1. ∀R:predicate lenv. R L1 →
-                (∀L,L2. ⦃h, L1⦄ ⊢ ➡*[g] L → ⦃h, L⦄ ⊢ ➡[g] L2 → R L → R L2) →
-                ∀L2. ⦃h, L1⦄ ⊢ ➡*[g] L2 → R L2.
+                (∀L,L2. ⦃h, L1⦄ ⊢ ➡*[h, g] L → ⦃G, L⦄ ⊢ ➡[h, g] L2 → R L → R L2) →
+                ∀L2. ⦃h, L1⦄ ⊢ ➡*[h, g] L2 → R L2.
 #h #g #L1 #R #HL1 #IHL1 #L2 #HL12
 @(TC_star_ind … HL1 IHL1 … HL12) //
 qed-.
 
 lemma lpxs_ind_dx: ∀h,g,L2. ∀R:predicate lenv. R L2 →
-                   (∀L1,L. ⦃h, L1⦄ ⊢ ➡[g] L → ⦃h, L⦄ ⊢ ➡*[g] L2 → R L → R L1) →
-                   ∀L1. ⦃h, L1⦄ ⊢ ➡*[g] L2 → R L1.
+                   (∀L1,L. ⦃h, L1⦄ ⊢ ➡[h, g] L → ⦃G, L⦄ ⊢ ➡*[h, g] L2 → R L → R L1) →
+                   ∀L1. ⦃h, L1⦄ ⊢ ➡*[h, g] L2 → R L1.
 #h #g #L2 #R #HL2 #IHL2 #L1 #HL12
 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lprs_lpxs: ∀h,g,L1,L2. L1 ⊢ ➡* L2 → ⦃h, L1⦄ ⊢ ➡*[g] L2.
+lemma lprs_lpxs: ∀h,g,L1,L2. L1 ⊢ ➡* L2 → ⦃h, L1⦄ ⊢ ➡*[h, g] L2.
 /3 width=3/ qed.
 
-lemma lpx_lpxs: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → ⦃h, L1⦄ ⊢ ➡*[g] L2.
+lemma lpx_lpxs: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[h, g] L2 → ⦃h, L1⦄ ⊢ ➡*[h, g] L2.
 /2 width=1/ qed.
 
-lemma lpxs_refl: ∀h,g,L. ⦃h, L⦄ ⊢ ➡*[g] L.
+lemma lpxs_refl: ∀h,g,L. ⦃G, L⦄ ⊢ ➡*[h, g] L.
 /2 width=1/ qed.
 
-lemma lpxs_strap1: ∀h,g,L1,L,L2. ⦃h, L1⦄ ⊢ ➡*[g] L → ⦃h, L⦄ ⊢ ➡[g] L2 → ⦃h, L1⦄ ⊢ ➡*[g] L2.
+lemma lpxs_strap1: ∀h,g,L1,L,L2. ⦃h, L1⦄ ⊢ ➡*[h, g] L → ⦃G, L⦄ ⊢ ➡[h, g] L2 → ⦃h, L1⦄ ⊢ ➡*[h, g] L2.
 /2 width=3/ qed.
 
-lemma lpxs_strap2: ∀h,g,L1,L,L2. ⦃h, L1⦄ ⊢ ➡[g] L → ⦃h, L⦄ ⊢ ➡*[g] L2 → ⦃h, L1⦄ ⊢ ➡*[g] L2.
+lemma lpxs_strap2: ∀h,g,L1,L,L2. ⦃h, L1⦄ ⊢ ➡[h, g] L → ⦃G, L⦄ ⊢ ➡*[h, g] L2 → ⦃h, L1⦄ ⊢ ➡*[h, g] L2.
 /2 width=3/ qed.
 
-lemma lpxs_pair_refl: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡*[g] L2 → ∀I,V. ⦃h, L1. ⓑ{I}V⦄ ⊢ ➡*[g] L2. ⓑ{I}V.
+lemma lpxs_pair_refl: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡*[h, g] L2 → ∀I,V. ⦃h, L1. ⓑ{I}V⦄ ⊢ ➡*[h, g] L2. ⓑ{I}V.
 /2 width=1 by TC_lpx_sn_pair_refl/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lpxs_inv_atom1: ∀h,g,L2. ⦃h, ⋆⦄ ⊢ ➡*[g] L2 → L2 = ⋆.
+lemma lpxs_inv_atom1: ∀h,g,L2. ⦃h, ⋆⦄ ⊢ ➡*[h, g] L2 → L2 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom1/ qed-.
 
-lemma lpxs_inv_atom2: ∀h,g,L1. ⦃h, L1⦄ ⊢ ➡*[g] ⋆ → L1 = ⋆.
+lemma lpxs_inv_atom2: ∀h,g,L1. ⦃h, L1⦄ ⊢ ➡*[h, g] ⋆ → L1 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom2/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpxs_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡*[g] L2 → |L1| = |L2|.
+lemma lpxs_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡*[h, g] L2 → |L1| = |L2|.
 /2 width=2 by TC_lpx_sn_fwd_length/ qed-.