Who Cites covers var?
covers_var	Def covers_var(A;x) == fr:frame(). fr < fr A.frame | fr.var = x > & (a:Label. (a fr.acts) (ef:eff(). ef < ef A.eff | ef.kind = a & ef.smt.lbl = x > ))
	Thm* A:ioa{i:l}(), x:Label. covers_var(A;x) Prop
ioa_eff	Def t.eff == 1of(2of(2of(2of(2of(t)))))
	Thm* t:ioa{i:l}(). t.eff Collection(eff())
eff_smt	Def t.smt == 2of(2of(2of(t)))
	Thm* t:eff(). t.smt smt()
smt_lbl	Def t.lbl == 1of(t)
	Thm* t:smt(). t.lbl Label
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
eff	Def eff() == LabelLabelSimpleTypesmt()
	Thm* eff() Type
frame	Def frame() == LabelSimpleType(Label List)
	Thm* frame() Type
smt	Def smt() == LabelTermSimpleType
	Thm* smt() 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
assert	Def b == if b True else False fi
	Thm* b:. b Prop
eff_kind	Def t.kind == 1of(t)
	Thm* t:eff(). t.kind Label
col_filter	Def < x c | P(x) > (x) == x c & P(x)
	Thm* T:Type, c:Collection(T), Q:(TProp). < i c | Q(i) > Collection(T)
col_member	Def x c == c(x)
	Thm* T:Type, x:T, c:Collection(T). x c Prop
frame_acts	Def t.acts == 2of(2of(t))
	Thm* t:frame(). t.acts Label List
l_member	Def (x l) == i:. i < ||l|| & x = l[i] T
	Thm* T:Type, x:T, l:T List. (x l) Prop
ioa_frame	Def t.frame == 2of(2of(2of(2of(2of(t)))))
	Thm* t:ioa{i:l}(). t.frame Collection(frame())
frame_var	Def t.var == 1of(t)
	Thm* t:frame(). t.var Label
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
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)
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	Def Case(value) body == body(value,value)
eq_atom	Def x=yAtom == if x=yAtomtrue; false fi
	Thm* x,y:Atom. x=yAtom
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])
eq_int	Def i=j == if i=j true ; false fi
	Thm* i,j:. (i=j)
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])
case_ptn_atom	Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
ptn	Def Pattern == rec(T.ptn_con(T))
	Thm* Pattern Type
select	Def l[i] == hd(nth_tl(i;l))
	Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
	Thm* A:Type, l:A List. ||l||
	Thm* ||nil||
nat	Def == {i:| 0i }
	Thm* Type
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
nth_tl	Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive)
	Thm* A:Type, as:A List, i:. nth_tl(i;as) A List
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	Def Tree(E) == rec(T.tree_con(E;T))
	Thm* E:Type. Tree(E) Type
ptn_con	Def ptn_con(T) == Atom++Atom+(TT)
	Thm* T:Type. ptn_con(T) Type
le	Def AB == B < A
	Thm* i,j:. (ij) Prop
tree_con	Def tree_con(E;T) == E+(TT)
	Thm* E,T:Type. tree_con(E;T) Type
le_int	Def ij == j < i
	Thm* i,j:. (ij)
not	Def A == A False
	Thm* A:Prop. (A) Prop
lt_int	Def i < j == if i < j true ; false fi
	Thm* i,j:. (i < j)
bnot	Def b == if b false else true fi
	Thm* b:. b

Syntax:

covers_var(A;x)

has structure:

covers_var(A; x)

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