Nuprl Lemma : es-interval-partition
∀[es:EO]. ∀[e',e,a:E]. [e, e'] = ([e, pred(a)] @ [a, e']) ∈ (E List) supposing (e <loc a) ∧ a ≤loc e'
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
not: ¬A,
false: False,
so_apply: x[s],
guard: {T},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
iff: P ⇐⇒ Q,
or: P ∨ Q,
cand: A c∧ B,
top: Top,
squash: ↓T,
true: True,
rev_implies: P ⇐ Q
Latex:
\mforall{}[es:EO]. \mforall{}[e',e,a:E]. [e, e'] = ([e, pred(a)] @ [a, e']) supposing (e <loc a) \mwedge{} a \mleq{}loc e'
Date html generated:
2016_05_16-AM-09_33_52
Last ObjectModification:
2016_01_17-PM-01_29_33
Theory : new!event-ordering
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