Nuprl Lemma : latest-val-val
∀[Info:Type]
∀es:EO+(Info)
∀[T:Type]
∀X:EClass(T). ∀e:E.
∃e':E
(e' ≤loc e ∧ (↑e' ∈b X) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑e'' ∈b X))) ∧ ((X)-(e) = X(e') ∈ T))
supposing ↑e ∈b (X)-
Proof
Definitions occuring in Statement :
es-latest-val: (X)-,
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_witness,
in-eclass_wf,
es-latest-val_wf,
top_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
latest-val-cases,
es-le-self,
es-locl_transitivity2,
es-le_weakening,
es-locl_irreflexivity,
assert_wf,
es-locl_wf,
es-le_wf,
all_wf,
not_wf,
eclass-val_wf,
eclass_wf,
prior-val-val
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}e:E.
\mexists{}e':E
(e' \mleq{}loc e
\mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X)))
\mwedge{} ((X)\msupminus{}(e) = X(e')))
supposing \muparrow{}e \mmember{}\msubb{} (X)\msupminus{}
Date html generated:
2015_07_21-PM-03_23_09
Last ObjectModification:
2015_01_27-PM-06_45_04
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