Nuprl Lemma : primed-classrel-opt
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[b:Id ─→ bag(T)]. ∀[es:EO+(Info)]. ∀[v:T]. ∀[e:E].
uiff(v ∈ Prior(X)?b(e);↓∃e'<e.v ∈ X(e') ∧ ∀e''<e.∀w:T. (w ∈ X(e'') ⇒ e'' ≤loc e' )
∨ (v ↓∈ b loc(e) ∧ ∀e'<e.∀w:T. (¬w ∈ X(e'))))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-lt: ∀e<e'.P[e],
existse-before: ∃e<e'.P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
decidable__es-le,
decidable__es-locl,
es-le-not-locl,
bag-member_wf,
es-locl_wf,
es-E_wf,
alle-lt_wf,
Id_wf,
es-loc_wf,
all_wf,
es-le_wf,
event-ordering+_subtype,
not_wf,
assert_of_lt_int,
bag-size_wf,
nat_wf,
bag-member-iff-size,
assert_wf,
lt_int_wf,
existse-before_wf,
sq_stable__bag-member,
es-le_weakening_eq,
es-causle_antisymmetry,
es-causle_weakening_locl,
empty-bag-iff-no-member,
length_of_nil_lemma
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[b:Id {}\mrightarrow{} bag(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[v:T]. \mforall{}[e:E].
uiff(v \mmember{} Prior(X)?b(e);\mdownarrow{}\mexists{}e'<e.v \mmember{} X(e') \mwedge{} \mforall{}e''<e.\mforall{}w:T. (w \mmember{} X(e'') {}\mRightarrow{} e'' \mleq{}loc e' )
\mvee{} (v \mdownarrow{}\mmember{} b loc(e) \mwedge{} \mforall{}e'<e.\mforall{}w:T. (\mneg{}w \mmember{} X(e'))))
Date html generated:
2015_07_21-PM-03_18_59
Last ObjectModification:
2015_01_27-PM-07_26_51
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