{ 
[Info,A,B,S:Type]. [init:S]. [f:S 
A S]. [test:S A 
].
[nxt:S 
A S]. [g:S A (B?)]. [X:EClass(A)].
(g[Threshold(init;f;test;nxt;X)]
= 
p.threshold_val(p)[es-interface-accum(threshold_accum(test;
nxt;
f;
g);<init, inr 
>;X)]) }
{ Proof }
Definitions occuring in Statement :
es-threshold: Threshold(init;f;test;nxt;X),
es-interface-accum: es-interface-accum(f;x;X),
es-filter-image: f[X],
eclass: EClass(A[eo; e]),
threshold_val: threshold_val(p),
threshold_accum: threshold_accum,
bool: ,
it: ,
uall: [x:A]. B[x],
unit: Unit,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
product: x:A B[x],
inr: inr x ,
union: left + right,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
threshold_val: threshold_val(p),
member: t 
T,
so_lambda: 
x y.t[x; y],
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
top: Top,
assert: 
b,
subtype: S 
T,
btrue: tt,
true: True,
suptype: suptype(S; T),
bfalse: ff,
implies: P 
Q,
prop: 
,
squash: 
T,
so_lambda: x.t[x],
eclass: EClass(A[eo; e]),
es-interface-accum: es-interface-accum(f;x;X),
list_accum: list_accum(x,a.f[x; a];y;l),
ycomb: Y,
es-E-interface: E(X),
and: P 
Q,
threshold_accum: threshold_accum,
pi1: fst(t),
iff: P 
Q,
rev_implies: P Q,
cand: A c B,
so_apply: x[s1;s2],
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
bool: ,
unit: Unit,
so_apply: x[s],
nat: 
,
length: ||as||,
decidable: Dec(P),
or: P 
Q,
not: 
A,
false: False,
it:
Lemmas :
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
unit_wf,
bool_wf,
es-E-interface_wf,
es-interface-top,
es-threshold-image-as-accum,
eclass-val_wf,
subtype_base_sq,
bool_subtype_base,
top_wf,
assert_elim,
in-eclass_wf,
iff_weakening_uiff,
assert_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
es-filter-image_wf,
squash_wf,
true_wf,
pi2_wf,
ifthenelse_wf,
es-interface-predecessors_wf,
Id_wf,
es-loc_wf,
es-interface-predecessors-nonempty,
length_wf_nat,
nat_wf,
length_wf1,
member_wf,
list_accum_wf,
it_wf,
es-interface-accum_wf,
es-threshold_wf,
threshold_accum_wf,
es-interface-extensionality,
decidable__assert,
iff_wf,
es-interface-subtype_rel2,
can-apply_wf,
es-is-filter-image,
is-threshold,
es-interface-subtype_rel,
is-interface-accum
\mforall{}[Info,A,B,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{}[g:S \mtimes{} A {}\mrightarrow{} (B?)]. \mforall{}[X:EClass(A)].
(g[Threshold(init;f;test;nxt;X)]
= \mlambda{}p.threshold\_val(p)[es-interface-accum(threshold\_accum(test;
nxt;
f;
g);<init, inr \mcdot{} >X)])
Date html generated:
2011_08_16-PM-06_10_45
Last ObjectModification:
2010_11_10-AM-05_47_43
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