WhoCites Definitions mb event system 4 Sections EventSystems Doc
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Who Cites ma-decla?
ma-declaDef a declared in M == locl(a dom(1of(2of(M)))
Kind-deqDef KindDeq == union-deq(IdLnkId;Id;product-deq(IdLnk;Id;IdLnkDeq;IdDeq);IdDeq)
idlnk-deqDef IdLnkDeq == product-deq(Id;Id;IdDeq;product-deq(Id;;IdDeq;NatDeq))
id-deqDef IdDeq == product-deq(Atom;;AtomDeq;NatDeq)
product-deqDef product-deq(A;B;a;b) == <proddeq(a;b),prod-deq(A;B;a;b)>
proddeqDef proddeq(a;b)(p,q) == (1of(a)(1of(p),1of(q)))(1of(b)(2of(p),2of(q)))
Thm* A,B:Type, a:EqDecider(A), b:EqDecider(B). proddeq(a;b ABAB
pi2Def 2of(t) == t.2
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p B(1of(p))
fpf-domDef x  dom(f) == deq-member(eq;x;1of(f))
union-deqDef union-deq(A;B;a;b) == <sumdeq(a;b),sum-deq(A;B;a;b)>
deq-memberDef deq-member(eq;x;L) == reduce(a,b. eqof(eq)(a,x b;false;L)
sumdeqDef sumdeq(a;b)(p,q)
Def == InjCase(ppa. InjCase(qqa. 1of(a)(pa,qa); qb. false); pb.
Def == InjCase(qqa. falseqb. 1of(b)(pb,qb)))
Thm* A,B:Type, a:EqDecider(A), b:EqDecider(B). sumdeq(a;b (A+B)(A+B)
eqofDef eqof(d) == 1of(d)
Thm* T:Type, d:EqDecider(T). eqof(d TT
pi1Def 1of(t) == t.1
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p A
loclDef locl(a) == inr(a)
Thm* a:Id. locl(a Knd
prod-deqDef prod-deq(A;B;a;b)
Def == (A,B,a,b,p,qq/q1,q2.
Def == (p/p1,p2.
Def == (b/eq,b1.
Def == (a/e1,a1.
Def == ((%1.%1
Def == ((%1.(<%.<(%1.%1(p1,q1)/%4,%5%4((%1.%1)((%1.*)(*))))(a1)
Def == ((%1.(<%.,(%1.%1(p2,q2)/%4,%5%4((%1.%1)((%1.*)(*))))(b1)>
Def == ((%1.(,%.%/%1,%2*>))
Def == (((%1.%1.2)
Def == ((((%1.%1
Def == ((((%1.(<p1,p2> = <q1,q2 AB
Def == ((((%1.,<p1,p2> = <q1,q2 AB
Def == ((((%1.,((e1(p1,q1))(eq(p2,q2)))
Def == ((((%1.,(e1(p1,q1)) & (eq(p2,q2))
Def == ((((%1.,(%1.%1)((%1.<%2.%2,%2.%2>)(*))
Def == ((((%1.,(%1.%1)
Def == ((((%1.,((%1.%1(e1(p1,q1),eq(p2,q2)))
Def == ((((%1.,((p,q. InjCase(qx. InjCase(p
Def == ((((%1.,((p,q. InjCase(qx. InjCasex. <%.<*,*>,%.*>
Def == ((((%1.,((p,q. InjCase(qx. InjCasey. <%.<any(%),*>
Def == ((((%1.,((p,q. InjCase(qx. InjCase; y,%.%/%1,%2. any(%1)>)
Def == ((((%1.,((p,qy.
Def == ((((%1.,((p,qInjCase(p
Def == ((((%1.,((p,q. InjCasex. <%.<*,any(%)>,%.%/%1,%2. any(%2)>
Def == ((((%1.,((p,q. InjCasey. <%.<any(%),any(%)>
Def == ((((%1.,((p,q. InjCase; y,%.%/%1,%2. any(%2)>))))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(%5
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.((((%5
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.((((((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(((((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(((((((%6((%4.%4)((%4.%4)(%3))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(((((((%))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.((((%2))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.<%3.(%1)
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(%5
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.((((%6
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.((((((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(((((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(((((((%6((%4.%4)((%4.%4)(%3))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(((((((%1))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.((((%2))))
Def == ((((P1,P2,Q1,Q2,%,%1. <%2.,%3.(%)>
Def == ((((P1,P2,Q1,Q2,%,%1,%2.<%3.(%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(%6
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.((((%5
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.((((((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(((((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(((((((%5((%4.%4)((%4.%4)(%3))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(((((((%))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.((((%2))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.<%3.(%1)
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(%6
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.((((%6
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.((((((%4.%4)
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(((((((%4.%4/%5,%6.
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(((((((%5((%4.%4)((%4.%4)(%3))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(((((((%1))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.((((%2))))
Def == ((((P1,P2,Q1,Q2,%,%1. ,%2.,%3.(%)>>))))
Def == (A
Def == ,B
Def == ,a
Def == ,b)
assertDef b == if b True else False fi
Thm* b:b  Prop
IdLnkDef IdLnk == IdId
Thm* IdLnk  Type
IdDef Id == Atom
Thm* Id  Type
nat-deqDef NatDeq == <a,ba=b,nat_DASH_deq_DASH_aux{1:l}>
atom-deqDef AtomDeq == <a,ba=bAtom,atom_DASH_deq_DASH_aux{1:l}>
natDef  == {i:| 0i }
Thm*   Type
sum-deqDef sum-deq(A;B;a;b)
Def == (A,B,a,b,p,q.
Def == (InjCase(qx. InjCase(p
Def == (InjCase(qx. InjCasex1b/eq,b1.
Def == (InjCase(qx. InjCase; x1a/e1,a1.
Def == (InjCase(qx. InjCase; x1<%.(%1.%1(x1,x)/%4,%5.
Def == (InjCase(qx. InjCase; x1. <%.(%4
Def == (InjCase(qx. InjCase; x1. <%.(((%1.%1)
Def == (InjCase(qx. InjCase; x1. <%.((((%1.*)
Def == (InjCase(qx. InjCase; x1. <%.(((((%1.%1(x))
Def == (InjCase(qx. InjCase; x1. <%.((((((%1.%1(x1))
Def == (InjCase(qx. InjCase; x1. <%.(((((((%1.%1(B))
Def == (InjCase(qx. InjCase; x1. <%.((((((((%1.%1(A))
Def == (InjCase(qx. InjCase; x1. <%.((((((((A,B,x1,x,%. (%1.%1)
Def == (InjCase(qx. InjCase; x1. <%.((((((((A,B,x1,x,%((%1.(%2.*)(*))
Def == (InjCase(qx. InjCase; x1. <%.((((((((A,B,x1,x,%. ((%))))))))))
Def == (InjCase(qx. InjCase; x1. <%.(a1)
Def == (InjCase(qx. InjCase; x1,%.*>
Def == (InjCase(qx. InjCaseyb/eq,b1.
Def == (InjCase(qx. InjCase; ya/e1,a1.
Def == (InjCase(qx. InjCase; y<%.(%1.any((%1(*))))
Def == (InjCase(qx. InjCase; y. <%.((%1.%1(x))
Def == (InjCase(qx. InjCase; y. <%.(((%1.%1(y))
Def == (InjCase(qx. InjCase; y. <%.((((%1.%1(B))
Def == (InjCase(qx. InjCase; y. <%.(((((%1.%1(A))
Def == (InjCase(qx. InjCase; y. <%.(((((A,B,y,x,%.
Def == (InjCase(qx. InjCase; y. <%.((((((%1.
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase(%1
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase%2. any(%2)
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase%3. (%4.any(%4))
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase; %3((%4.(%5.(%6.
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase; %3. ((%4.(%5.(any(%6))
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase; %3. ((%4.(%5.(*))
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase; %3. ((%4.(*))
Def == (InjCase(qx. InjCase; y. <%.((((((InjCase; %3. ((%))))
Def == (InjCase(qx. InjCase; y. <%.(((((((%1.%1)(inr(%.*))))))))
Def == (InjCase(qx. InjCase; y,%.*>)
Def == (y.
Def == (InjCase(p
Def == (InjCasexb/eq,b1.
Def == (InjCase; xa/e1,a1.
Def == (InjCase; x<%.(%1.any((%1(*))))
Def == (InjCase; x. <%.((%1.%1(y))
Def == (InjCase; x. <%.(((%1.%1(x))
Def == (InjCase; x. <%.((((%1.%1(B))
Def == (InjCase; x. <%.(((((%1.%1(A))
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase(%1
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase%2. any(%2)
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase%3. (%4.any(%4))
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase; %3((%4.(%5.(%6.
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase; %3. ((%4.(%5.(any(%6))
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase; %3. ((%4.(%5.(*))
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase; %3. ((%4.(*))
Def == (InjCase; x. <%.(((((A,B,x,y,%. (%1.InjCase; %3. ((%))))
Def == (InjCase; x. <%.(((((A,B,x,y,%((%1.%1)(inr(%.*))))))))
Def == (InjCase; x,%.*>
Def == (InjCasey1b/eq,b1.
Def == (InjCase; y1a/e1,a1.
Def == (InjCase; y1<%.(%1.%1(y1,y)/%4,%5.
Def == (InjCase; y1. <%.(%4
Def == (InjCase; y1. <%.(((%1.%1)
Def == (InjCase; y1. <%.((((%1.*)
Def == (InjCase; y1. <%.(((((%1.%1(y))
Def == (InjCase; y1. <%.((((((%1.%1(y1))
Def == (InjCase; y1. <%.(((((((%1.%1(B))
Def == (InjCase; y1. <%.((((((((%1.%1(A))
Def == (InjCase; y1. <%.((((((((A,B,y1,y,%. (%1.%1)
Def == (InjCase; y1. <%.((((((((A,B,y1,y,%((%1.(%2.*)(*))(%))))))))))
Def == (InjCase; y1. <%.(b1)
Def == (InjCase; y1,%.*>)))
Def == (A
Def == ,B
Def == ,a
Def == ,b)
borDef p  q == if p true else q fi
Thm* p,q:. (p  q 
reduceDef reduce(f;k;as) == Case of as; nil  k ; a.as'  f(a,reduce(f;k;as'))
Def (recursive)
Thm* A,B:Type, f:(ABB), k:Bas:A List. reduce(f;k;as B
eq_intDef i=j == if i=j true ; false fi
Thm* i,j:. (i=j 
eq_atomDef x=yAtom == if x=yAtomtrue; false fi
Thm* x,y:Atom. x=yAtom  
leDef AB == B<A
Thm* i,j:. (ij Prop
bandDef pq == if p q else false fi
Thm* p,q:. (pq 
notDef A == A  False
Thm* A:Prop. (A Prop

Syntax:a declared in M has structure: ma-decla(Ma)

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assertintnatural_numberint_eqless_thanatomatom_equnion
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falsetrueall!abstraction
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WhoCites Definitions mb event system 4 Sections EventSystems Doc