Nuprl Lemma : loop-class-memory-exists-prior
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(0 < #(init loc(e));↓∃v:B. v ∈ Prior(loop-class-memory(X;init))?init(e))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
primed-class-opt: Prior(X)?b,
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,
uiff: uiff(P;Q),
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 :
less_than_wf,
bag-size_wf,
es-loc_wf,
event-ordering+_subtype,
nat_wf,
squash_wf,
exists_wf,
classrel_wf,
primed-class-opt_wf,
loop-class-memory_wf,
member-less_than,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
decidable__assert,
es-first_wf2,
bag-member-iff-size,
primed-class-opt-classrel,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-locl_wf,
es-p-local-pred_wf,
es-pred-loc-base,
iff_weakening_equal,
loop-class-memory-exists,
es-pred_wf,
es-pred-locl,
es-pred_property,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-causl_transitivity2,
es-causle_weakening,
es-causl_irreflexivity,
all_wf,
not_wf,
bag-member_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].
uiff(0 < \#(init loc(e));\mdownarrow{}\mexists{}v:B. v \mmember{} Prior(loop-class-memory(X;init))?init(e))
Date html generated:
2015_07_21-PM-02_35_29
Last ObjectModification:
2015_02_04-PM-06_20_55
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