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. 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,
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)
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
less_than_wf,
es-E_wf,
decidable__lt,
subtract_wf,
false_wf,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
less-iff-le,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
es-causl_wf,
decidable__assert,
es-first_wf2,
exists_wf,
bag-member_wf,
es-loc_wf,
single-valued-bag_wf,
all_wf,
nat_wf,
iterated_classrel_wf,
set_wf,
primrec-wf2,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
add-zero,
decidable__exists-single-valued-classrel,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
classrel_wf,
not_wf,
or_wf,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
squash_wf,
true_wf,
bag_wf,
es-pred-loc-base,
iff_weakening_equal,
assert-bnot,
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. iterated\_classrel(es;S;A;f;init;X;e;v)))
Date html generated:
2015_07_17-PM-00_23_33
Last ObjectModification:
2015_02_04-PM-05_36_35
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