Nuprl Lemma : iterated_classrel-exists-iff
[Info,A,S:Type]. [init:Id 
bag(S)]. [f:A S S]. [X:EClass(A)]. [es:EO+(Info)]. [e:E].
uiff(
s:S. s 
init loc(e);v:S. v X*(f,init,e))
Proof not projected
Definitions occuring in Statement :
iterated_classrel: v X*(f,init,e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
exists: x:A. B[x],
squash: T,
apply: f a,
function: x:A B[x],
universe: Type,
bag-member: x bs,
bag: bag(T)
Definitions :
uiff: uiff(P;Q),
squash: T,
exists: x:A. B[x],
and: P 
Q,
uimplies: b supposing a,
member: t T,
true: True,
so_lambda: 
x.t[x],
implies: P 
Q,
all: x:A. B[x],
nat: 
,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
so_lambda: x y.t[x; y],
iterated_classrel: v X*(f,init,e),
uall: [x:A]. B[x],
prop: 
,
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
ycomb: Y,
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
or: P 
Q,
btrue: tt,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
subtype: S 
T
Lemmas :
iterated_classrel-exists,
squash_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
es-causl-swellfnd,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
equal_wf,
iterated_classrel_wf,
es-first_wf,
event-ordering+_inc,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
es-pred_wf,
es-pred-causl,
es-loc-pred,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
and_wf
\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].
uiff(\mdownarrow{}\mexists{}s:S. s \mdownarrow{}\mmember{} init loc(e);\mdownarrow{}\mexists{}v:S. v \mmember{} X*(f,init,e))
Date html generated:
2012_01_23-PM-12_19_58
Last ObjectModification:
2012_01_18-AM-00_39_40
Home
Index