Nuprl Lemma : existse-between3_wf
∀[es:EO]. ∀[e1,e2:E]. ∀[P:{e:E| (loc(e) = loc(e1) ∈ Id) ∧ (¬↑first(e))} ⟶ ℙ].
∃e∈(e1,e2].P[e] ∈ ℙ supposing loc(e2) = loc(e1) ∈ Id
Proof
Definitions occuring in Statement :
existse-between3: ∃e∈(e1,e2].P[e],
es-first: first(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
not: ¬A,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
existse-between3: ∃e∈(e1,e2].P[e],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
cand: A c∧ B,
and: P ∧ Q,
so_apply: x[s],
es-locl: (e <loc e'),
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[P:\{e:E| (loc(e) = loc(e1)) \mwedge{} (\mneg{}\muparrow{}first(e))\} {}\mrightarrow{} \mBbbP{}].
\mexists{}e\mmember{}(e1,e2].P[e] \mmember{} \mBbbP{} supposing loc(e2) = loc(e1)
Date html generated:
2016_05_16-AM-09_45_42
Last ObjectModification:
2015_12_28-PM-09_38_16
Theory : new!event-ordering
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