Nuprl Lemma : member-es-interface-history
∀[Info:Type]
∀es:EO+(Info)
∀[A:Type]
∀X:EClass(A List). ∀e:E. ∀a:A.
((a ∈ es-interface-history(es;X;e)) ⇐⇒ ∃e':E. (((↑e' ∈b X) ∧ e' ≤loc e ) ∧ (a ∈ X(e'))))
Proof
Definitions occuring in Statement :
es-interface-history: es-interface-history(es;X;e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Lemmas :
member-es-le-before2,
event-ordering+_subtype,
es-le_wf,
l_member_wf,
es-E_wf,
Id_wf,
es-loc_wf,
es-le-before_wf,
iff_wf,
exists_wf,
list_wf,
assert_wf,
in-eclass_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
subtype_top,
eclass-val_wf,
member-mapfilter,
set_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
mapfilter_wf,
es-E-interface-property,
member-concat,
concat_wf,
eclass_wf,
squash_wf,
true_wf,
iff_weakening_equal,
es-le-loc
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A List). \mforall{}e:E. \mforall{}a:A.
((a \mmember{} es-interface-history(es;X;e)) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. (((\muparrow{}e' \mmember{}\msubb{} X) \mwedge{} e' \mleq{}loc e ) \mwedge{} (a \mmember{} X(e'))))
Date html generated:
2015_07_20-PM-03_40_01
Last ObjectModification:
2015_02_04-PM-05_30_42
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