Nuprl Lemma : primed-classrel
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[v:T]. ∀[e:E].
uiff(v ∈ Prior(X)(e);↓∃e'<e.v ∈ X(e') ∧ ∀e''<e.∀w:T. (w ∈ X(e'') ⇒ e'' ≤loc e' ))
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
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-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type
Lemmas :
classrel_wf,
primed-class_wf,
squash_wf,
existse-before_wf,
event-ordering+_subtype,
Id_wf,
es-loc_wf,
es-E_wf,
alle-lt_wf,
all_wf,
es-le_wf,
event-ordering+_wf,
eclass_wf,
es-local-pred_wf,
lt_int_wf,
bag-size_wf,
nat_wf,
or_wf,
sq_exists_wf,
es-locl_wf,
assert_wf,
not_wf,
bag-member_wf,
bag-member-empty,
empty-bag_wf,
equal_wf,
decidable__es-le,
decidable__es-locl,
es-le-not-locl,
assert_of_lt_int,
bag-member-iff-size,
sq_stable__bag-member,
es-le_weakening_eq,
es-causle_antisymmetry,
es-causle_weakening_locl
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[v:T]. \mforall{}[e:E].
uiff(v \mmember{} Prior(X)(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' ))
Date html generated:
2015_07_21-PM-03_18_44
Last ObjectModification:
2015_01_27-PM-07_25_35
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