Nuprl Lemma : es-before-partition
∀[es:EO]. ∀[e,e':E]. before(e) = (≤loc(e') @ (e', e)) ∈ (E List) supposing (e' <loc e)
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-le-before: ≤loc(e),
es-before: before(e),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
es-le-before: ≤loc(e),
top: Top,
true: True,
or: P ∨ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
squash: ↓T
Latex:
\mforall{}[es:EO]. \mforall{}[e,e':E]. before(e) = (\mleq{}loc(e') @ (e', e)) supposing (e' <loc e)
Date html generated:
2016_05_16-AM-09_35_29
Last ObjectModification:
2016_01_17-PM-01_28_01
Theory : new!event-ordering
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