X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fdama%2Fclassical_pointwise%2Fsets.ma;h=f03c3e7f21d87e85952614efb8d8b6f35c14a6d4;hb=db068aa35cc47bb881ec810bf3b904c3d7cc9379;hp=ec6a1c77456c32f3355291ab730bb4c16afbd705;hpb=df666eb58afe0b312a2c4d41683d7ae4828ee8bd;p=helm.git diff --git a/matita/dama/classical_pointwise/sets.ma b/matita/dama/classical_pointwise/sets.ma index ec6a1c774..f03c3e7f2 100644 --- a/matita/dama/classical_pointwise/sets.ma +++ b/matita/dama/classical_pointwise/sets.ma @@ -12,9 +12,11 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/sets/". + include "nat/nat.ma". +include "logic/connectives.ma". + definition set ≝ λX:Type.X → Prop. @@ -24,21 +26,21 @@ notation "hvbox(x break ∈ A)" with precedence 60 for @{ 'member_of $x $A }. interpretation "Member of" 'member_of x A = - (cic:/matita/sets/member_of.con _ A x). + (cic:/matita/classical_pointwise/sets/member_of.con _ A x). notation "hvbox(x break ∉ A)" with precedence 60 for @{ 'not_member_of $x $A }. interpretation "Not member of" 'not_member_of x A = (cic:/matita/logic/connectives/Not.con - (cic:/matita/sets/member_of.con _ A x)). + (cic:/matita/classical_pointwise/sets/member_of.con _ A x)). definition emptyset : ∀X.set X ≝ λX:Type.λx:X.False. notation "∅︀" with precedence 100 for @{ 'emptyset }. interpretation "Emptyset" 'emptyset = - (cic:/matita/sets/emptyset.con _). + (cic:/matita/classical_pointwise/sets/emptyset.con _). definition subset: ∀X. set X → set X → Prop≝ λX.λA,B:set X.∀x. x ∈ A → x ∈ B. @@ -46,7 +48,7 @@ notation "hvbox(A break ⊆ B)" with precedence 60 for @{ 'subset $A $B }. interpretation "Subset" 'subset A B = - (cic:/matita/sets/subset.con _ A B). + (cic:/matita/classical_pointwise/sets/subset.con _ A B). definition intersection: ∀X. set X → set X → set X ≝ λX.λA,B:set X.λx. x ∈ A ∧ x ∈ B. @@ -55,7 +57,7 @@ notation "hvbox(A break ∩ B)" with precedence 70 for @{ 'intersection $A $B }. interpretation "Intersection" 'intersection A B = - (cic:/matita/sets/intersection.con _ A B). + (cic:/matita/classical_pointwise/sets/intersection.con _ A B). definition union: ∀X. set X → set X → set X ≝ λX.λA,B:set X.λx. x ∈ A ∨ x ∈ B. @@ -63,7 +65,7 @@ notation "hvbox(A break ∪ B)" with precedence 65 for @{ 'union $A $B }. interpretation "Union" 'union A B = - (cic:/matita/sets/union.con _ A B). + (cic:/matita/classical_pointwise/sets/union.con _ A B). definition seq ≝ λX:Type.nat → X. @@ -73,7 +75,7 @@ notation "hvbox(A \sub i)" with precedence 100 for @{ 'nth $A $i }. interpretation "nth" 'nth A i = - (cic:/matita/sets/nth.con _ A i). + (cic:/matita/classical_pointwise/sets/nth.con _ A i). definition countable_union: ∀X. seq (set X) → set X ≝ λX.λA:seq (set X).λx.∃j.x ∈ A \sub j. @@ -82,7 +84,7 @@ notation "∪ \sub (ident i opt (: ty)) B" with precedence 65 for @{ 'big_union ${default @{(λ${ident i}:$ty.$B)} @{(λ${ident i}.$B)}}}. interpretation "countable_union" 'big_union η.t = - (cic:/matita/sets/countable_union.con _ t). + (cic:/matita/classical_pointwise/sets/countable_union.con _ t). definition complement: ∀X. set X \to set X ≝ λX.λA:set X.λx. x ∉ A. @@ -90,7 +92,7 @@ notation "A \sup 'c'" with precedence 100 for @{ 'complement $A }. interpretation "Complement" 'complement A = - (cic:/matita/sets/complement.con _ A). + (cic:/matita/classical_pointwise/sets/complement.con _ A). definition inverse_image: ∀X,Y.∀f: X → Y.set Y → set X ≝ λX,Y,f,B,x. f x ∈ B. @@ -99,4 +101,4 @@ notation "hvbox(f \sup (-1))" with precedence 100 for @{ 'finverse $f }. interpretation "Inverse image" 'finverse f = - (cic:/matita/sets/inverse_image.con _ _ f). \ No newline at end of file + (cic:/matita/classical_pointwise/sets/inverse_image.con _ _ f).