X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fdama%2Fdama%2Funiform.ma;h=25cfe67cb6da3e02adbfd4283078c1f619708d21;hb=9eabe046c1182960de8cfdba96c5414224e3a61e;hp=41b593ae4a25832cc073a98c0702235f1c39be84;hpb=c3b8ed2e554cbdb677729747c5b5a96112ae5169;p=helm.git diff --git a/helm/software/matita/contribs/dama/dama/uniform.ma b/helm/software/matita/contribs/dama/dama/uniform.ma index 41b593ae4..25cfe67cb 100644 --- a/helm/software/matita/contribs/dama/dama/uniform.ma +++ b/helm/software/matita/contribs/dama/dama/uniform.ma @@ -29,23 +29,19 @@ definition subset ≝ λO:bishop_set.λP,Q:O→Prop.∀x:O.P x → Q x. notation "a \subseteq u" left associative with precedence 70 for @{ 'subset $a $u }. -interpretation "Bishop subset" 'subset a b = - (cic:/matita/dama/uniform/subset.con _ a b). +interpretation "Bishop subset" 'subset a b = (subset _ a b). notation "hvbox({ ident x : t | break p })" non associative with precedence 50 for @{ 'explicitset (\lambda ${ident x} : $t . $p) }. definition mk_set ≝ λT:bishop_set.λx:T→Prop.x. -interpretation "explicit set" 'explicitset t = - (cic:/matita/dama/uniform/mk_set.con _ t). +interpretation "explicit set" 'explicitset t = (mk_set _ t). notation < "s 2 \atop \neq" non associative with precedence 90 for @{ 'square2 $s }. notation > "s 'square'" non associative with precedence 90 for @{ 'square $s }. -interpretation "bishop set square" 'square x = - (cic:/matita/dama/uniform/square_bishop_set.con x). -interpretation "bishop set square" 'square2 x = - (cic:/matita/dama/uniform/square_bishop_set.con x). +interpretation "bishop set square" 'square x = (square_bishop_set x). +interpretation "bishop set square" 'square2 x = (square_bishop_set x). alias symbol "exists" = "exists". @@ -56,12 +52,11 @@ definition compose_relations ≝ notation "a \circ b" left associative with precedence 60 for @{'compose $a $b}. -interpretation "relations composition" 'compose a b = - (cic:/matita/dama/uniform/compose_relations.con _ a b). +interpretation "relations composition" 'compose a b = (compose_relations _ a b). notation "hvbox(x \in break a \circ break b)" non associative with precedence 50 for @{'compose2 $a $b $x}. interpretation "relations composition" 'compose2 a b x = - (cic:/matita/dama/uniform/compose_relations.con _ a b x). + (compose_relations _ a b x). definition invert_relation ≝ λC:bishop_set.λU:C square → Prop. @@ -73,10 +68,8 @@ notation < "s \sup (-1) x" non associative with precedence 90 for @{ 'invert2 $s $x}. notation > "'inv' s" non associative with precedence 90 for @{ 'invert $s }. -interpretation "relation invertion" 'invert a = - (cic:/matita/dama/uniform/invert_relation.con _ a). -interpretation "relation invertion" 'invert2 a x = - (cic:/matita/dama/uniform/invert_relation.con _ a x). +interpretation "relation invertion" 'invert a = (invert_relation _ a). +interpretation "relation invertion" 'invert2 a x = (invert_relation _ a x). alias symbol "exists" = "CProp exists". alias symbol "and" (instance 18) = "constructive and". @@ -103,8 +96,7 @@ notation < "a \nbsp 'is_cauchy'" non associative with precedence 50 for @{'cauchy $a}. notation > "a 'is_cauchy'" non associative with precedence 50 for @{'cauchy $a}. -interpretation "Cauchy sequence" 'cauchy s = - (cic:/matita/dama/uniform/cauchy.con _ s). +interpretation "Cauchy sequence" 'cauchy s = (cauchy _ s). (* Definition 2.15 *) definition uniform_converge ≝ @@ -116,7 +108,7 @@ notation < "a \nbsp (\u \atop (\horbar\triangleright)) \nbsp x" non associative notation > "a 'uniform_converges' x" non associative with precedence 50 for @{'uniform_converge $a $x}. interpretation "Uniform convergence" 'uniform_converge s u = - (cic:/matita/dama/uniform/uniform_converge.con _ s u). + (uniform_converge _ s u). (* Lemma 2.16 *) lemma uniform_converge_is_cauchy : @@ -133,8 +125,7 @@ qed. (* Definition 2.17 *) definition mk_big_set ≝ λP:CProp.λF:P→CProp.F. -interpretation "explicit big set" 'explicitset t = - (cic:/matita/dama/uniform/mk_big_set.con _ t). +interpretation "explicit big set" 'explicitset t = (mk_big_set _ t). definition restrict_uniformity ≝ λC:uniform_space.λX:C→Prop.