Nuprl Lemma : alle-between2-not-first-since
∀[es:EO]. ∀[e1:E]. ∀[e2:{e:E| loc(e) = loc(e1) ∈ Id} ]. ∀[p:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ].
uiff(∀e∈[e1,e2].¬e = first e ≥ e1.p[e];∀e∈[e1,e2].¬p[e])
Proof
Definitions occuring in Statement :
es-first-since: e2 = first e ≥ e1.P[e],
alle-between2: ∀e∈[e1,e2].P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
not: ¬A,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
alle-between2: ∀e∈[e1,e2].P[e],
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
es-first-since: e2 = first e ≥ e1.P[e],
cand: A c∧ B,
alle-between1: ∀e∈[e1,e2).P[e]
Latex:
\mforall{}[es:EO]. \mforall{}[e1:E]. \mforall{}[e2:\{e:E| loc(e) = loc(e1)\} ]. \mforall{}[p:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
uiff(\mforall{}e\mmember{}[e1,e2].\mneg{}e = first e \mgeq{} e1.p[e];\mforall{}e\mmember{}[e1,e2].\mneg{}p[e])
Date html generated:
2016_05_16-AM-09_54_44
Last ObjectModification:
2015_12_28-PM-09_32_27
Theory : new!event-ordering
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