Nuprl Lemma : l_before-es-interval
∀es:EO. ∀e,e',a,b:E. (a before b ∈ [e, e'] ⇐⇒ (a <loc b) ∧ e ≤loc a ∧ b ≤loc e' )
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
l_before: x before y ∈ l,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
es-interval: [e, e'],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
false: False,
uimplies: b supposing a,
es-le: e ≤loc e' ,
cand: A c∧ B
Latex:
\mforall{}es:EO. \mforall{}e,e',a,b:E. (a before b \mmember{} [e, e'] \mLeftarrow{}{}\mRightarrow{} (a <loc b) \mwedge{} e \mleq{}loc a \mwedge{} b \mleq{}loc e' )
Date html generated:
2016_05_16-AM-09_32_13
Last ObjectModification:
2015_12_28-PM-09_50_01
Theory : new!event-ordering
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