{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [X:EClass(A)]. [S:Type].
[init:S]. [f:S 
A S]. [test:S A 
]. [nxt:S 
A S]. [e:E].
[s:S]. [v:A].
{(
e 
X) 
(v = X(e))}
supposing Threshold(init;f;test;nxt;X)(e) = <s, v>
supposing e Threshold(init;f;test;nxt;X) }
{ Proof }
Definitions occuring in Statement :
es-threshold: Threshold(init;f;test;nxt;X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
and: P Q,
function: x:A B[x],
pair: <a, b>,
product: x:A B[x],
universe: Type,
equal: s = t
Definitions :
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
axiom: Ax,
implies: P 
Q,
false: False,
true: True,
and: P Q,
guard: {T},
pair: <a, b>,
eclass-val: X(e),
limited-type: LimitedType,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
void: Void,
es-E-interface: E(X),
es-threshold: Threshold(init;f;test;nxt;X),
in-eclass: e X,
prop: 
,
assert: b,
uimplies: b supposing a,
product: x:A B[x],
bool: ,
union: left + right,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
cand: A c B,
cond-class: [X?Y],
so_apply: x[s],
or: P 
Q,
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
es-prior-interface-vals: X(<e),
es-prior-interval-vals: X(e1, e2),
list_accum: list_accum(x,a.f[x; a];y;l),
let: let,
es-prior-interface: prior(X),
fpf: a:A fp-> B[a],
list: type List,
pi2: snd(t),
so_lambda: x.t[x],
set: {x:A| B[x]}
Lemmas :
pi2_wf,
es-threshold-val2,
uiff_inversion,
assert_wf,
guard_wf,
assert_witness,
es-threshold_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-E_wf,
eclass-val_wf,
top_wf,
subtype_rel_wf,
es-interface-subtype_rel2,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
bool_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[S:Type]. \mforall{}[init:S]. \mforall{}[f:S {}\mrightarrow{} A {}\mrightarrow{} S].
\mforall{}[test:S {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}]. \mforall{}[nxt:S \mtimes{} A {}\mrightarrow{} S]. \mforall{}[e:E].
\mforall{}[s:S]. \mforall{}[v:A]. \{(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (v = X(e))\} supposing Threshold(init;f;test;nxt;X)(e) = <s, v>
supposing \muparrow{}e \mmember{}\msubb{} Threshold(init;f;test;nxt;X)
Date html generated:
2011_08_16-PM-05_11_49
Last ObjectModification:
2011_06_20-AM-01_13_37
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