commit by user andrea

diff --git a/weblib/basics/relations.ma b/weblib/basics/relations.ma
index 995198aac2483ee8a56cb720ea609f8a1739ed0f..753ed32332d9e51f4a09f306ac9b929c103e96d3 100644 (file)
--- a/weblib/basics/relations.ma
+++ b/weblib/basics/relations.ma
@@ -12,78 +12,78 @@
 include "basics/logic.ma".
 
 (********** relations **********)
-\ 5img class="anchor" src="icons/tick.png" id="relation"\ 6definition relation : Type[0] → Type[0]
+definition relation : Type[0] → Type[0]
 ≝ λA.A→A→Prop. 
 
-\ 5img class="anchor" src="icons/tick.png" id="reflexive"\ 6definition reflexive: ∀A.∀R :\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition reflexive: ∀A.∀R :\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x:A.R x x.
 
-\ 5img class="anchor" src="icons/tick.png" id="symmetric"\ 6definition symmetric: ∀A.∀R: \ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition symmetric: ∀A.∀R: \ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x,y:A.R x y → R y x.
 
-\ 5img class="anchor" src="icons/tick.png" id="transitive"\ 6definition transitive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition transitive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x,y,z:A.R x y → R y z → R x z.
 
-\ 5img class="anchor" src="icons/tick.png" id="irreflexive"\ 6definition irreflexive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition irreflexive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x:A.\ 5a title="logical not" href="cic:/fakeuri.def(1)"\ 6¬\ 5/a\ 6(R x x).
 
-\ 5img class="anchor" src="icons/tick.png" id="cotransitive"\ 6definition cotransitive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition cotransitive: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x,y:A.R x y → ∀z:A. R x z \ 5a title="logical or" href="cic:/fakeuri.def(1)"\ 6∨\ 5/a\ 6 R z y.
 
-\ 5img class="anchor" src="icons/tick.png" id="tight_apart"\ 6definition tight_apart: ∀A.∀eq,ap:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition tight_apart: ∀A.∀eq,ap:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λeq,ap.∀x,y:A. (\ 5a title="logical not" href="cic:/fakeuri.def(1)"\ 6¬\ 5/a\ 6(ap x y) → eq x y) \ 5a title="logical and" href="cic:/fakeuri.def(1)"\ 6∧\ 5/a\ 6
 (eq x y → \ 5a title="logical not" href="cic:/fakeuri.def(1)"\ 6¬\ 5/a\ 6(ap x y)).
 
-\ 5img class="anchor" src="icons/tick.png" id="antisymmetric"\ 6definition antisymmetric: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
+definition antisymmetric: ∀A.∀R:\ 5a href="cic:/matita/basics/relations/relation.def(1)"\ 6relation\ 5/a\ 6 A.Prop
 ≝ λA.λR.∀x,y:A. R x y → \ 5a title="logical not" href="cic:/fakeuri.def(1)"\ 6¬\ 5/a\ 6(R y x).
 
 (********** functions **********)
 
-\ 5img class="anchor" src="icons/tick.png" id="compose"\ 6definition compose ≝
+definition compose ≝
   λA,B,C:Type[0].λf:B→C.λg:A→B.λx:A.f (g x).
 
 interpretation "function composition" 'compose f g = (compose ? ? ? f g).
 
-\ 5img class="anchor" src="icons/tick.png" id="injective"\ 6definition injective: ∀A,B:Type[0].∀ f:A→B.Prop
+definition injective: ∀A,B:Type[0].∀ f:A→B.Prop
 ≝ λA,B.λf.∀x,y:A.f x \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 f y → x\ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6y.
 
-\ 5img class="anchor" src="icons/tick.png" id="surjective"\ 6definition surjective: ∀A,B:Type[0].∀f:A→B.Prop
+definition surjective: ∀A,B:Type[0].∀f:A→B.Prop
 ≝λA,B.λf.∀z:B.\ 5a title="exists" href="cic:/fakeuri.def(1)"\ 6∃\ 5/a\ 6x:A\ 5a title="exists" href="cic:/fakeuri.def(1)"\ 6.\ 5/a\ 6z \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 f x.
 
-\ 5img class="anchor" src="icons/tick.png" id="commutative"\ 6definition commutative: ∀A:Type[0].∀f:A→A→A.Prop 
+definition commutative: ∀A:Type[0].∀f:A→A→A.Prop 
 ≝ λA.λf.∀x,y.f x y \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 f y x.
 
-\ 5img class="anchor" src="icons/tick.png" id="commutative2"\ 6definition commutative2: ∀A,B:Type[0].∀f:A→A→B.Prop
+definition commutative2: ∀A,B:Type[0].∀f:A→A→B.Prop
 ≝ λA,B.λf.∀x,y.f x y \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 f y x.
 
-\ 5img class="anchor" src="icons/tick.png" id="associative"\ 6definition associative: ∀A:Type[0].∀f:A→A→A.Prop
+definition associative: ∀A:Type[0].∀f:A→A→A.Prop
 ≝ λA.λf.∀x,y,z.f (f x y) z \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 f x (f y z).
 
 (* functions and relations *)
-\ 5img class="anchor" src="icons/tick.png" id="monotonic"\ 6definition monotonic : ∀A:Type[0].∀R:A→A→Prop.
+definition monotonic : ∀A:Type[0].∀R:A→A→Prop.
 ∀f:A→A.Prop ≝
 λA.λR.λf.∀x,y:A.R x y → R (f x) (f y).
 
 (* functions and functions *)
-\ 5img class="anchor" src="icons/tick.png" id="distributive"\ 6definition distributive: ∀A:Type[0].∀f,g:A→A→A.Prop
+definition distributive: ∀A:Type[0].∀f,g:A→A→A.Prop
 ≝ λA.λf,g.∀x,y,z:A. f x (g y z) \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 g (f x y) (f x z).
 
-\ 5img class="anchor" src="icons/tick.png" id="distributive2"\ 6definition distributive2: ∀A,B:Type[0].∀f:A→B→B.∀g:B→B→B.Prop
+definition distributive2: ∀A,B:Type[0].∀f:A→B→B.∀g:B→B→B.Prop
 ≝ λA,B.λf,g.∀x:A.∀y,z:B. f x (g y z) \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 g (f x y) (f x z).
 
-\ 5img class="anchor" src="icons/tick.png" id="injective_compose"\ 6lemma injective_compose : ∀A,B,C,f,g.
+lemma injective_compose : ∀A,B,C,f,g.
 \ 5a href="cic:/matita/basics/relations/injective.def(1)"\ 6injective\ 5/a\ 6 A B f → \ 5a href="cic:/matita/basics/relations/injective.def(1)"\ 6injective\ 5/a\ 6 B C g → \ 5a href="cic:/matita/basics/relations/injective.def(1)"\ 6injective\ 5/a\ 6 A C (λx.g (f x)).
 /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5/span\ 6\ 5/span\ 6/; qed.
 
 (* extensional equality *)
 
-\ 5img class="anchor" src="icons/tick.png" id="exteqP"\ 6definition exteqP: ∀A:Type[0].∀P,Q:A→Prop.Prop ≝
+definition exteqP: ∀A:Type[0].∀P,Q:A→Prop.Prop ≝
 λA.λP,Q.∀a.\ 5a href="cic:/matita/basics/logic/iff.def(1)"\ 6iff\ 5/a\ 6 (P a) (Q a).
 
-\ 5img class="anchor" src="icons/tick.png" id="exteqR"\ 6definition exteqR: ∀A,B:Type[0].∀R,S:A→B→Prop.Prop ≝
+definition exteqR: ∀A,B:Type[0].∀R,S:A→B→Prop.Prop ≝
 λA,B.λR,S.∀a.∀b.\ 5a href="cic:/matita/basics/logic/iff.def(1)"\ 6iff\ 5/a\ 6 (R a b) (S a b).
 
-\ 5img class="anchor" src="icons/tick.png" id="exteqF"\ 6definition exteqF: ∀A,B:Type[0].∀f,g:A→B.Prop ≝
+definition exteqF: ∀A,B:Type[0].∀f,g:A→B.Prop ≝
 λA,B.λf,g.∀a.f a \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 g a.
 
 notation " x \eqP y " non associative with precedence 45