Nuprl Lemma : es-minimal-event
∀es:EO
∀[P:E ⟶ ℙ]. ((∀e:E. Dec(P[e])) ⇒ (∀e:E. (P[e] ⇒ (∃m:E. (m ≤loc e ∧ P[m] ∧ (∀e':E. ((e' <loc m) ⇒ (¬P[e']))))))))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
uimplies: b supposing a,
alle-at: ∀e@i.P[e],
decidable: Dec(P),
or: P ∨ Q,
existse-before: ∃e<e'.P[e],
cand: A c∧ B,
not: ¬A,
false: False
Latex:
\mforall{}es:EO
\mforall{}[P:E {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E. Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. (P[e] {}\mRightarrow{} (\mexists{}m:E. (m \mleq{}loc e \mwedge{} P[m] \mwedge{} (\mforall{}e':E. ((e' <loc m) {}\mRightarrow{} (\mneg{}P[e']))))))))
Date html generated:
2016_05_16-AM-09_41_32
Last ObjectModification:
2015_12_28-PM-09_42_45
Theory : new!event-ordering
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