Nuprl Lemma : iterated-classrel-exists
∀[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],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
decidable__exists-single-valued-classrel,
iterated-classrel_wf,
exists_wf,
or_wf,
es-loc_wf,
bag-member_wf,
not_wf,
all_wf,
classrel_wf,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
bool_wf,
event-ordering+_subtype,
es-first_wf2,
iff_weakening_equal,
es-E_wf,
es-pred-loc-base,
bag_wf,
true_wf,
squash_wf,
es-causl_weakening,
es-pred-locl,
es-pred_wf,
assert-bnot
\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))
{}\mRightarrow{} (\mexists{}v:S. iterated-classrel(es;S;A;f;init;X;e;v)))
Date html generated:
2015_07_17-PM-00_26_38
Last ObjectModification:
2015_07_16-AM-09_43_58
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