update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_inclusion.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_inclusion.ma
index 7fd5fd4188da4d10e655c3caf7228af676327907..adc3fa667ff983dd6b574359daa1498fa65ab8d1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_inclusion.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext_inclusion.ma
@@ -14,17 +14,43 @@
 
 include "ground/lib/subset_inclusion.ma".
 include "ground/lib/subset_ext.ma".
+include "ground/lib/exteq.ma".
 
 (* EXTENSIONS FOR SUBSETS ***************************************************)
 
 (* Constructions with subset_inclusion **************************************)
 
+lemma subset_inclusion_ext_f1_exteq (A1) (A0) (f1) (f2) (u):
+      f1 ⊜ f2 → subset_ext_f1 A1 A0 f1 u ⊆ subset_ext_f1 A1 A0 f2 u.
+#A1 #A0 #f1 #f2 #u #Hf #a0 * #a1 #Hau1 #H destruct
+/2 width=1 by subset_in_ext_f1_dx/
+qed.
+
 lemma subset_inclusion_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 #a0 * #a1 #Hau1 #H destruct
 /3 width=3 by subset_in_ext_f1_dx/
 qed.
 
+lemma subset_inclusion_ext_f1_compose_sn (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.
+#A0 #A1 #A2 #f1 #f2 #u #a2 * #a1 * #a0 #Ha0 #H1 #H2 destruct
+/2 width=1 by subset_in_ext_f1_dx/
+qed.
+
+lemma subset_inclusion_ext_f1_compose_dx (A0) (A1) (A2) (f1) (f2) (u):
+      subset_ext_f1 A0 A2 (f2∘f1) u ⊆ subset_ext_f1 A1 A2 f2 (subset_ext_f1 A0 A1 f1 u).
+#A0 #A1 #A2 #f1 #f2 #u #a2 * #a0 #Ha0 #H0 destruct
+/3 width=1 by subset_in_ext_f1_dx/
+qed.
+
+lemma subset_inclusion_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 #Huv21 #a0 *
+/3 width=3 by subset_inclusion_ext_f1_bi, or_introl, or_intror/
+qed.
+
 lemma subset_inclusion_ext_p1_trans (A1) (Q) (u1) (v1):
       u1 ⊆ v1 → subset_ext_p1 A1 Q v1 → subset_ext_p1 A1 Q u1.
 #A1 #Q #u1 #v1 #Huv1 #Hv1