Nuprl Lemma : es-causl-p-locl-test
∀es:EO. ∀p:E ⟶ (E + Top). (causal-predecessor(es;p) ⇒ (∀e,e',a,b:E. (a c≤ e ⇒ e p≤ e' ⇒ e' p< b ⇒ (a < b))))
Proof
Definitions occuring in Statement :
es-p-le: e p≤ e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
es-causle: e c≤ e',
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top).
(causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e',a,b:E. (a c\mleq{} e {}\mRightarrow{} e p\mleq{} e' {}\mRightarrow{} e' p< b {}\mRightarrow{} (a < b))))
Date html generated:
2016_05_16-AM-10_32_01
Last ObjectModification:
2016_01_06-PM-02_27_55
Theory : new!event-ordering
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