Nuprl Lemma : l_before-es-le-before-iff
∀the_es:EO. ∀e,e',y:E. (e' before y ∈ ≤loc(e) ⇐⇒ (e' <loc y) ∧ y ≤loc e )
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(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-le-before: ≤loc(e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
guard: {T},
uimplies: b supposing a,
es-le: e ≤loc e' ,
cand: A c∧ B
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e,e',y:E. (e' before y \mmember{} \mleq{}loc(e) \mLeftarrow{}{}\mRightarrow{} (e' <loc y) \mwedge{} y \mleq{}loc e )
Date html generated:
2016_05_16-AM-09_31_03
Last ObjectModification:
2015_12_28-PM-09_49_47
Theory : new!event-ordering
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