Nuprl Lemma : null-es-hist
∀[Info:Type]. ∀es:EO+(Info). ∀e1,e2:E. ↑null(es-hist(es;e1;e2)) ⇐⇒ (e2 <loc e1) supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
Id: Id,
null: null(as),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
top: Top,
prop: ℙ,
rev_implies: P ⇐ Q,
es-hist: es-hist(es;e1;e2),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
not: ¬A,
false: False,
uiff: uiff(P;Q)
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e1,e2:E. \muparrow{}null(es-hist(es;e1;e2)) \mLeftarrow{}{}\mRightarrow{} (e2 <loc e1) supposing loc(e2) = loc(e1)
Date html generated:
2016_05_16-PM-01_19_03
Last ObjectModification:
2016_01_17-PM-07_55_29
Theory : event-ordering
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