Nuprl Lemma : Memory-class-exists
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
↓∃v:B. v ∈ Memory-class(f;init;X)(e) supposing 0 < #(init loc(e))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
bag-size_wf,
es-loc_wf,
nat_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
es-causl_wf,
decidable__assert,
es-first_wf2,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
Memory-class_wf,
classrel_wf,
es-pred_wf,
iterated-classrel_wf,
assert_wf,
not_wf,
Memory-classrel2,
bag-member-iff-size,
iff_weakening_equal,
es-pred-loc-base,
true_wf,
squash_wf,
es-causl_weakening,
es-pred-locl,
bag-member_wf,
all_wf,
or_wf,
exists_wf,
le_weakening,
empty-bag-iff-size,
empty-bag-iff-no-member,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
bool_wf
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mdownarrow{}\mexists{}v:B. v \mmember{} Memory-class(f;init;X)(e) supposing 0 < \#(init loc(e))
Date html generated:
2015_07_22-PM-00_12_49
Last ObjectModification:
2015_07_16-AM-09_39_49
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