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.
(single-valued-classrel(es;X;A) ⇒ (∃s:S. s ↓∈ init loc(e) ⇐⇒ ∃v:S. iterated-classrel(es;S;A;f;init;X;e;v)))
Proof
Definitions occuring in Statement :
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
iterated-classrel-exists,
exists_wf,
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
es-causl-swellfnd,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-first_wf2,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
iterated-classrel_wf,
squash_wf,
true_wf,
bag_wf,
es-pred-loc-base,
es-E_wf,
iff_weakening_equal,
equal_wf,
all_wf,
int_seg_subtype-nat,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
single-valued-classrel_wf,
event-ordering+_wf,
eclass_wf,
Id_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.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} (\mexists{}s:S. s \mdownarrow{}\mmember{} init loc(e) \mLeftarrow{}{}\mRightarrow{} \mexists{}v:S. iterated-classrel(es;S;A;f;init;X;e;v)))
Date html generated:
2015_07_17-PM-00_26_46
Last ObjectModification:
2015_02_04-PM-05_34_44
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