update in ground

+ additions to subset extensionality

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma
index 5d623ad16f3afa6e60c2080b71f9a5bf6b6d3c27..5839bfb108d754e7cd2cd4f7d2fdba00a0d1aac6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma
@@ -19,6 +19,11 @@ include "ground/lib/subset.ma".
 definition subset_ext_f1 (A1) (A0) (f:A1→A0): 𝒫❨A1❩ → 𝒫❨A0❩ ≝
            λu1,a0. ∃∃a1. a1 ϵ u1 & f a1 = a0.
 
+definition subset_ext_f1_1 (A11) (A21) (A0) (f1:A11→A0) (f2:A21→A0): 𝒫❨A11❩ → 𝒫❨A21❩ → 𝒫❨A0❩ ≝
+           λu11,u21,a0.
+           ∨∨ subset_ext_f1 A11 A0 f1 u11 a0
+            | subset_ext_f1 A21 A0 f2 u21 a0.
+
 definition subset_ext_p1 (A1) (Q:predicate A1): predicate (𝒫❨A1❩) ≝
            λu1. ∀a1. a1 ϵ u1 → Q a1.
 
@@ -28,6 +33,14 @@ lemma subset_in_ext_f1_dx (A1) (A0) (f) (u1) (a1):
       a1 ϵ u1 → f a1 ϵ subset_ext_f1 A1 A0 f u1.
 /2 width=3 by ex2_intro/ qed.
 
+lemma subset_in_ext_f1_1_dx_1 (A11) (A21) (A0) (f1) (f2) (u11) (u21) (a11):
+      a11 ϵ u11 → f1 a11 ϵ subset_ext_f1_1 A11 A21 A0 f1 f2 u11 u21.
+/3 width=3 by subset_in_ext_f1_dx, or_introl/ qed.
+
+lemma subset_in_ext_f1_1_dx_2 (A11) (A21) (A0) (f1) (f2) (u11) (u21) (a21):
+      a21 ϵ u21 → f2 a21 ϵ subset_ext_f1_1 A11 A21 A0 f1 f2 u11 u21.
+/3 width=3 by subset_in_ext_f1_dx, or_intror/ qed.
+
 (* Basic inversions *********************************************************)
 
 lemma subset_in_inv_ext_p1_dx (A1) (Q) (u1) (a1):

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 28e4facc8fada42dea5249abc964c86f9f87a6e3..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
@@ -30,6 +30,13 @@ lemma subset_equivalence_ext_f1_bi (A1) (A0) (f) (u1) (v1):
 /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/

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 f16fc373a77bcba518c1d9f5ec91978f33f9f84f..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
@@ -44,6 +44,13 @@ lemma subset_inclusion_ext_f1_compose_dx (A0) (A1) (A2) (f1) (f2) (u):
 /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