Nuprl Lemma : member-loop-class-memory
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
(e ∈b loop-class-memory(X;init) ~ 0 <z #(init loc(e)))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs),
bag: bag(T)
Lemmas :
bool_cases_sqequal,
member-eclass_wf,
loop-class-memory_wf,
sqequal-tt-to-assert,
lt_int_wf,
bag-size_wf,
es-loc_wf,
nat_wf,
loop-class-memory-member,
sqequal-ff-to-assert,
subtype_base_sq,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
assert_of_lt_int,
true_wf,
false_wf,
less_than_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(e \mmember{}\msubb{} loop-class-memory(X;init) \msim{} 0 <z \#(init loc(e)))
Date html generated:
2015_07_23-AM-11_28_45
Last ObjectModification:
2015_01_28-PM-11_13_24
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