update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / subset_ext_equivalence.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_equivalence.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_equivalence.ma
index f20aca24fc2903e33d300817be8825d7d15800e8..07df6b3e9793b56732cb5a261ed7aa3db3ee5c4e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_equivalence.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_equivalence.ma
@@ -19,8 +19,25 @@ include "ground/lib/subset_equivalence.ma".
 
 (* Constructions with subset_equivalence ************************************)
 
+lemma subset_equivalence_ext_f1_exteq (A1) (A0) (f1) (f2) (u):
+      f1 ⊜ f2 → subset_ext_f1 A1 A0 f1 u ⇔ subset_ext_f1 A1 A0 f2 u.
+/3 width=3 by subset_inclusion_ext_f1_exteq, conj/
+qed.
+
 lemma subset_equivalence_ext_f1_bi (A1) (A0) (f) (u1) (v1):
       u1 ⇔ v1 → subset_ext_f1 A1 A0 f u1 ⇔ subset_ext_f1 A1 A0 f v1.
 #A1 #A0 #f #u1 #v1 * #Huv1 #Hvu1
 /3 width=3 by subset_inclusion_ext_f1_bi, conj/
 qed.
+
+lemma subset_equivalence_ext_f1_1_bi (A11) (A21) (A0) (f1) (f2) (u11) (u21) (v11) (v21):
+      u11 ⇔ v11 → u21 ⇔ v21 →
+      subset_ext_f1_1 A11 A21 A0 f1 f2 u11 u21 ⇔ subset_ext_f1_1 A11 A21 A0 f1 f2 v11 v21.
+#A11 #A21 #A0 #f1 #f2 #u11 #u21 #v11 #v21 * #Huv11 #Hvu11 * #Huv21 #Hvu21
+/3 width=5 by subset_inclusion_ext_f1_1_bi, conj/
+qed.
+
+lemma subset_inclusion_ext_f1_compose (A0) (A1) (A2) (f1) (f2) (u):
+      subset_ext_f1 A1 A2 f2 (subset_ext_f1 A0 A1 f1 u) ⇔ subset_ext_f1 A0 A2 (f2∘f1) u.
+/3 width=1 by subset_inclusion_ext_f1_compose_dx, subset_inclusion_ext_f1_compose_sn, conj/
+qed.