- star.ma: strip lemma and confluence of star

[helm.git] / matita / matita / contribs / lambda / term.ma

diff --git a/matita/matita/contribs/lambda/term.ma b/matita/matita/contribs/lambda/term.ma
index 92a838fb4cbe8b8f3bccdef807e66a817f20b307..2e08b861e1b8206839a0a9c93bdb376c3269d34f 100644 (file)
--- a/matita/matita/contribs/lambda/term.ma
+++ b/matita/matita/contribs/lambda/term.ma
@@ -47,12 +47,33 @@ notation "hvbox( 𝛌  . term 46 A )"
 notation "hvbox( @ term 46 C . break term 46 A )"
    non associative with precedence 46
    for @{ 'Application $C $A }.
-(*
-definition appl_compatible_dx: predicate (relation term) ≝ λR.
-                               ∀B,A1,A2. R A1 A2 → R (@B.A1) (@B.A2).
 
-lemma star_appl_compatible_dx: ∀R. appl_compatible_dx R →
-                               appl_compatible_dx (star … R).
+definition compatible_abst: predicate (relation term) ≝ λR.
+                            ∀A1,A2. R A1 A2 → R (𝛌.A1) (𝛌.A2).
+
+definition compatible_sn: predicate (relation term) ≝ λR.
+                          ∀A,B1,B2. R B1 B2 → R (@B1.A) (@B2.A).
+
+definition compatible_dx: predicate (relation term) ≝ λR.
+                          ∀B,A1,A2. R A1 A2 → R (@B.A1) (@B.A2).
+
+definition compatible_appl: predicate (relation term) ≝ λR.
+                            ∀B1,B2. R B1 B2 → ∀A1,A2. R A1 A2 →
+                            R (@B1.A1) (@B2.A2).
+
+lemma star_compatible_abst: ∀R. compatible_abst R → compatible_abst (star … R).
+#R #HR #A1 #A2 #H elim H -A2 // /3 width=3/
+qed.
+
+lemma star_compatible_sn: ∀R. compatible_sn R → compatible_sn (star … R).
+#R #HR #A #B1 #B2 #H elim H -B2 // /3 width=3/
+qed.
+
+lemma star_compatible_dx: ∀R. compatible_dx R → compatible_dx (star … R).
 #R #HR #B #A1 #A2 #H elim H -A2 // /3 width=3/
 qed.
-*)
+
+lemma star_compatible_appl: ∀R. reflexive ? R →
+                            compatible_appl R → compatible_appl (star … R).
+#R #H1R #H2R #B1 #B2 #H elim H -B2 /3 width=1/ /3 width=5/
+qed.