Who Cites decl?
decl	Def Decl == LabelType
	Thm* Decl{i} Type{i'}
record_pair	Def {p} == {1of(p)}{2of(p)}
	Thm* p:(DeclDecl). {p} Type
record	Def {d} == l:Labeldecl_type(d;l)
	Thm* d:Decl. {d} Type
decl_type	Def decl_type(d;x) == d(x)
	Thm* dec:Decl, x:Label. decl_type(dec;x) Type
decls_mng	Def [[ds]] rho == [[d]] rho for d {d:dec()| d ds }
	Thm* ds:Collection(dec()), rho:Decl. [[ds]] rho Decl
ioa	Def ioa{i:l}() == Collection(dec())Collection(dec())Collection(rel())Collection(pre())Collection(eff())Collection(frame())
	Thm* ioa{i:l}() Type{i'}
ioa_all	Def ioa_all(I; i.A(i)) == mk_ioa(i:I. A(i).ds, i:I. A(i).da, i:I. A(i).init, i:I. A(i).pre, i:I. A(i).eff, i:I. A(i).frame)
	Thm* I:Type, A:(Iioa{i:l}()). ioa_all(I; i.A(i)) ioa{i:l}()
ioa_ds	Def t.ds == 1of(t)
	Thm* t:ioa{i:l}(). t.ds Collection(dec())
sig	Def sig() == (LabelSimpleType)(Label(SimpleType List))
	Thm* sig() Type
dec	Def dec() == LabelSimpleType
	Thm* dec() Type
frame	Def frame() == LabelSimpleType(Label List)
	Thm* frame() Type
eff	Def eff() == LabelLabelSimpleTypesmt()
	Thm* eff() Type
pre	Def pre() == LabelLabelrel()
	Thm* pre() Type
rel	Def rel() == relname()(Term List)
	Thm* rel() Type
smt	Def smt() == LabelTermSimpleType
	Thm* smt() Type
relname	Def relname() == SimpleType+Label
	Thm* relname() Type
st	Def SimpleType == Tree(Label+Unit)
	Thm* SimpleType Type
term	Def Term == Tree(ts())
	Thm* Term Type
ts	Def ts() == Label+Label+Label+Label+Label
	Thm* ts() Type
lbl	Def Label == {p:Pattern| ground_ptn(p) }
	Thm* Label Type
sig_mng	Def [[s]] rho == < op.[[s.fun(op)]] rho,R.[[s.rel(R)]] rho >
	Thm* s:sig(), rho:Decl{i}. sig_mng{i:l}(s; rho) Decl{i}Decl{i'}
subtype	Def S T == x:S. x T
dec_mng	Def [[d]] rho == Case(d) Case x : s = > x:[[s]] rho
	Thm* rho:Decl, d:dec(). [[d]] rho Decl
col_union	Def (i:I. C(i))(x) == i:I. x C(i)
	Thm* T,I:Type, C:(ICollection(T)). (i:I. C(i)) Collection(T)
col_member	Def x c == c(x)
	Thm* T:Type, x:T, c:Collection(T). x c Prop
dall	Def D(i) for i I(x) == i:I. D(i)(x)
	Thm* I:Type, D:(IDecl). D(i) for i I Decl
col	Def Collection(T) == TProp
	Thm* T:Type{i'}. Collection{i}(T) Type{i'}
ioa_frame	Def t.frame == 2of(2of(2of(2of(2of(t)))))
	Thm* t:ioa{i:l}(). t.frame Collection(frame())
ioa_eff	Def t.eff == 1of(2of(2of(2of(2of(t)))))
	Thm* t:ioa{i:l}(). t.eff Collection(eff())
ioa_pre	Def t.pre == 1of(2of(2of(2of(t))))
	Thm* t:ioa{i:l}(). t.pre Collection(pre())
ioa_init	Def t.init == 1of(2of(2of(t)))
	Thm* t:ioa{i:l}(). t.init Collection(rel())
	Thm* t:ioa{i:l}(). t.init Fmla
ioa_da	Def t.da == 1of(2of(t))
	Thm* t:ioa{i:l}(). t.da Collection(dec())
mk_ioa	Def mk_ioa(ds, da, init, pre, eff, frame) == < ds,da,init,pre,eff,frame >
	Thm* ds,da:Collection(dec()), init:Collection(rel()), pre:Collection(pre()), eff:Collection(eff()), frame:Collection(frame()). mk_ioa(ds, da, init, pre, eff, frame) ioa{i:l}()
sig_fun	Def t.fun == 1of(t)
	Thm* t:sig(). t.fun LabelSimpleType
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
ground_ptn	Def ground_ptn(p) == Case(p) Case ptn_var(v) = > false Case ptn_pr( < x, y > ) = > ground_ptn(x)ground_ptn(y) Default = > true (recursive)
	Thm* p:Pattern. ground_ptn(p)
assert	Def b == if b True else False fi
	Thm* b:. b Prop
ptn	Def Pattern == rec(T.ptn_con(T))
	Thm* Pattern Type
sig_rel	Def t.rel == 2of(t)
	Thm* t:sig(). t.rel Label(SimpleType List)
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
st_list_mng	Def [[l]] rho == reduce(s,m. [[s]] rhom;Prop;l)
	Thm* l:SimpleType List, rho:Decl{i}. [[l]] rho{i} Type{i'}
st_mng	Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s)
	Thm* rho:Decl, s:SimpleType. [[s]] rho Type
dbase	Def x:y(a) == if a = x y else Top fi
	Thm* x:Label, y:Type. x:y Decl
case_mk_dec	Def Case lbl : typ = > body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1)
t_iterate	Def t_iterate(l;n;t) == Case(t) Case x;y = > n(t_iterate(l;n;x),t_iterate(l;n;y)) Case tree_leaf(x) = > l(x) Default = > True (recursive)
	Thm* E,A:Type, l:(EA), n:(AAA), t:Tree(E). t_iterate(l;n;t) A
eq_lbl	Def l1 = l2 == Case(l1) Case ptn_atom(x) = > Case(l2) Case ptn_atom(y) = > x=yAtom Default = > false Case ptn_int(x) = > Case(l2) Case ptn_int(y) = > x=y Default = > false Case ptn_var(x) = > Case(l2) Case ptn_var(y) = > x=yAtom Default = > false Case ptn_pr( < x, y > ) = > Case(l2) Case ptn_pr( < u, v > ) = > x = uy = v Default = > false Default = > false (recursive)
	Thm* l1,l2:Pattern. l1 = l2
case	Def Case(value) body == body(value,value)
case_default	Def Default = > body(value,value) == body
band	Def pq == if p q else false fi
	Thm* p,q:. (pq)
case_lbl_pair	Def Case ptn_pr( < x, y > ) = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. InjCase(x2; _. cont(z,z); x2@0. InjCase(x2@0; _. cont(z,z); x2@1. x2@1/x3,x2@2. body(x3;x2@2))))
case_ptn_var	Def Case ptn_var(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
ptn_con	Def ptn_con(T) == Atom++Atom+(TT)
	Thm* T:Type. ptn_con(T) Type
tree	Def Tree(E) == rec(T.tree_con(E;T))
	Thm* E:Type. Tree(E) Type
reduce	Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as')) (recursive)
	Thm* A,B:Type, f:(ABB), k:B, as:A List. reduce(f;k;as) B
st_lift	Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top)
	Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type
top	Def Top == Void given Void
	Thm* Top Type
case_ptn_int	Def Case ptn_int(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
hd	Def hd(l) == Case of l; nil "?" ; h.t h
	Thm* A:Type, l:A List. ||l||1 hd(l) A
	Thm* A:Type, l:A List. hd(l) A
tl	Def tl(l) == Case of l; nil nil ; h.t t
	Thm* A:Type, l:A List. tl(l) A List
case_inl	Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))
case_inr	Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
tree_con	Def tree_con(E;T) == E+(TT)
	Thm* E,T:Type. tree_con(E;T) Type
case_tree_leaf	Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case_node	Def Case x;y = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0))
eq_atom	Def x=yAtom == if x=yAtomtrue; false fi
	Thm* x,y:Atom. x=yAtom
eq_int	Def i=j == if i=j true ; false fi
	Thm* i,j:. (i=j)
case_ptn_atom	Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))

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