some renaming and some typos corrected ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index ab498fc6395fc35ddaadd05d9b52abae58489e2a..4aeecb1185d436373a80194bc4a2bfd20c313b92 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -18,9 +18,9 @@ include "basic_2/substitution/drop.ma".
 (* RESTRICTED LOCAL ENVIRONMENT REFINEMENT **********************************)
 
 inductive lsubr: relation lenv ≝
-| lsubr_sort: ∀L. lsubr L (⋆)
-| lsubr_bind: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubr_abst: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
+| lsubr_atom: ∀L. lsubr L (⋆)
+| lsubr_pair: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| lsubr_beta: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
@@ -30,7 +30,7 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma lsubr_refl: ∀L. L ⫃ L.
-#L elim L -L /2 width=1 by lsubr_sort, lsubr_bind/
+#L elim L -L /2 width=1 by lsubr_atom, lsubr_pair/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -77,7 +77,7 @@ lemma lsubr_fwd_length: ∀L1,L2. L1 ⫃ L2 → |L2| ≤ |L1|.
 #L1 #L2 #H elim H -L1 -L2 /2 width=1 by monotonic_le_plus_l/
 qed-.
 
-lemma lsubr_fwd_drop2_bind: ∀L1,L2. L1 ⫃ L2 →
+lemma lsubr_fwd_drop2_pair: ∀L1,L2. L1 ⫃ L2 →
                             ∀I,K2,W,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓑ{I}W →
                             (∃∃K1. K1 ⫃ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓑ{I}W) ∨
                             ∃∃K1,V. K1 ⫃ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓓⓝW.V & I = Abst.
@@ -102,6 +102,6 @@ qed-.
 lemma lsubr_fwd_drop2_abbr: ∀L1,L2. L1 ⫃ L2 →
                             ∀K2,V,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓓV →
                             ∃∃K1. K1 ⫃ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓓV.
-#L1 #L2 #HL12 #K2 #V #s #i #HLK2 elim (lsubr_fwd_drop2_bind … HL12 … HLK2) -L2 // *
+#L1 #L2 #HL12 #K2 #V #s #i #HLK2 elim (lsubr_fwd_drop2_pair … HL12 … HLK2) -L2 // *
 #K1 #W #_ #_ #H destruct
 qed-.