Nuprl Lemma : es-closed-open-interval-decomp-member
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e1,e2,e:E]. [e1;e2) = ([e1;e) @ [e;e2)) ∈ (E List) supposing (e ∈ [e1, e2])
Proof
Definitions occuring in Statement :
event-ordering+: EO+(Info),
es-closed-open-interval: [e;e'),
es-interval: [e, e'],
es-E: E,
l_member: (x ∈ l),
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
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],
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e1,e2,e:E]. [e1;e2) = ([e1;e) @ [e;e2)) supposing (e \mmember{} [e1, e2])
Date html generated:
2016_05_16-PM-01_13_13
Last ObjectModification:
2015_12_29-PM-01_53_10
Theory : event-ordering
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