Nuprl Lemma : member-class-le-before
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:T].
uiff(v ↓∈ class-le-before(X;es;e);↓∃e':E. (e' ≤loc e ∧ v ∈ X(e')))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
class-le-before: class-le-before(X;es;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs
Lemmas :
es-le-before_wf,
event-ordering+_subtype,
list-subtype-bag,
es-E_wf,
Id_wf,
es-loc_wf,
bag-member-combine,
es-le_wf,
classrel_wf,
bag-member_wf,
bag-combine_wf,
squash_wf,
exists_wf,
class-le-before_wf,
event-ordering+_wf,
eclass_wf,
bag-member-list,
decidable__equal-es-E,
es-le-before_wf2,
subtype_rel_list,
member-es-le-before
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mdownarrow{}\mmember{} class-le-before(X;es;e);\mdownarrow{}\mexists{}e':E. (e' \mleq{}loc e \mwedge{} v \mmember{} X(e')))
Date html generated:
2015_07_17-PM-00_28_46
Last ObjectModification:
2015_01_27-PM-11_33_46
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