auto with intro

[helm.git] / helm / software / matita / nlibrary / topology / igft.ma

diff --git a/helm/software/matita/nlibrary/topology/igft.ma b/helm/software/matita/nlibrary/topology/igft.ma
index 81aefd555f02c320104e47f3d272fbf5301c6673..59ccd56019a34b690063b71f830dfbed5729b4ea 100644 (file)
--- a/helm/software/matita/nlibrary/topology/igft.ma
+++ b/helm/software/matita/nlibrary/topology/igft.ma
@@ -116,26 +116,6 @@ D*)
 
 include "sets/sets.ma".
 
-(*HIDE*)
-(* move away *)
-nlemma subseteq_intersection_l: ∀A.∀U,V,W:Ω^A.U ⊆ W ∨ V ⊆ W → U ∩ V ⊆ W.
-#A; #U; #V; #W; *; #H; #x; *; #xU; #xV; napply H; nassumption;
-nqed.
-
-nlemma subseteq_union_l: ∀A.∀U,V,W:Ω^A.U ⊆ W → V ⊆ W → U ∪ V ⊆ W.
-#A; #U; #V; #W; #H; #H1; #x; *; #Hx; ##[ napply H; ##| napply H1; ##] nassumption;
-nqed. 
-
-nlemma subseteq_intersection_r: ∀A.∀U,V,W:Ω^A.W ⊆ U → W ⊆ V → W ⊆ U ∩ V.
-#A; #U; #V; #W; #H1; #H2; #x; #Hx; @; ##[ napply H1; ##| napply H2; ##] nassumption;
-nqed. 
-
-ninductive sigma (A : Type[0]) (P : A → CProp[0]) : Type[0] ≝ 
- sig_intro : ∀x:A.P x → sigma A P. 
-
-interpretation "sigma" 'sigma \eta.p = (sigma ? p). 
-(*UNHIDE*)
-
 (*D
 
 Some basic results that we will use are also part of the sets library:
@@ -927,6 +907,9 @@ D*)
 alias symbol "covers" = "new covers set".
 alias symbol "covers" = "new covers".
 alias symbol "covers" = "new covers set".
+alias symbol "covers" = "new covers".
+alias symbol "covers" = "new covers set".
+alias symbol "covers" = "new covers".
 ntheorem new_coverage_infinity:
   ∀A:nAx.∀U:Ω^A.∀a:A. (∃i:𝐈 a. 𝐈𝐦[𝐝 a i] ◃ U) → a ◃ U.
 #A; #U; #a;                                   (** screenshot "n-cov-inf-1". *)  
@@ -1119,7 +1102,7 @@ before doing the induction over `o`.
 
 D*)
 ntheorem max_new_fished: 
-  ∀A:nAx.∀G:qpowerclass_setoid A.∀F:Ω^A.G ⊆ F → (∀a.a ∈ G → ∀i.𝐈𝐦[𝐝 a i] ≬ G) → G ⊆ ⋉F.
+  ∀A:nAx.∀G:ext_powerclass_setoid A.∀F:Ω^A.G ⊆ F → (∀a.a ∈ G → ∀i.𝐈𝐦[𝐝 a i] ≬ G) → G ⊆ ⋉F.
 #A; #G; #F; #GF; #H; #b; #HbG; #o; 
 ngeneralize in match HbG; ngeneralize in match b;
 nchange with (G ⊆ F⎽o);
@@ -1128,7 +1111,8 @@ nelim o;
 ##| #p; #IH; napply (subseteq_intersection_r … IH);
     #x; #Hx; #i; ncases (H … Hx i); #c; *; *; #d; #Ed; #cG;
     @d; napply IH;
-    napply (. Ed^-1‡#); napply cG;    
+    alias symbol "prop2" = "prop21".
+napply (. Ed^-1‡#); napply cG;    
 ##| #a; #i; #f; #Hf; nchange with (G ⊆ { y | ∀x. y ∈ F⎽(f x) }); 
     #b; #Hb; #d; napply (Hf d); napply Hb;
 ##]