Nuprl Lemma : decidable__exists_iterated_classrel
[Info,A,S:Type].
init:Id 
bag(S). f:A S S. X:EClass(A). es:EO+(Info). e:E.
(single-valued-classrel(es;X;A) 
single-valued-bag(init loc(e);S) Dec(
v:S. v 
X*(f,init,e)))
Proof not projected
Definitions occuring in Statement :
iterated_classrel: v X*(f,init,e),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
decidable: Dec(P),
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
decidable: Dec(P),
member: t T,
or: P 
Q,
so_lambda: 
x.t[x],
guard: {T},
so_lambda: x y.t[x; y],
nat: 
,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
squash: 
T,
true: True,
exists: x:A. B[x],
iterated_classrel: v X*(f,init,e),
ycomb: Y,
and: P 
Q,
ifthenelse: if b then t else f fi ,
cand: A c B,
btrue: tt,
bfalse: ff,
prop: 
,
so_apply: x[s],
so_apply: x[s1;s2],
strongwellfounded: SWellFounded(R[x; y]),
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype: S 
T,
it: 
Lemmas :
decidable__exists-single-valued-bag,
not_wf,
exists_wf,
iterated_classrel_wf,
single-valued-bag_wf,
es-loc_wf,
event-ordering+_inc,
single-valued-classrel_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
es-causl-swellfnd,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
decidable__assert,
es-first_wf,
bag-member_wf,
equal_wf,
decidable__exists-single-valued-classrel,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
assert_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
classrel_wf,
all_wf,
or_wf,
es-pred_wf,
es-pred-causl,
es-loc-pred,
and_wf,
ifthenelse_wf,
not_assert_elim,
iterated_classrel-exists-iff
\mforall{}[Info,A,S:Type].
\mforall{}init:Id {}\mrightarrow{} bag(S). \mforall{}f:A {}\mrightarrow{} S {}\mrightarrow{} S. \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e);S)
{}\mRightarrow{} Dec(\mexists{}v:S. v \mmember{} X*(f,init,e)))
Date html generated:
2012_01_23-PM-12_20_07
Last ObjectModification:
2012_01_18-AM-03_23_02
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