Nuprl Lemma : es-next
∀es:EO. ∀e,a:E. ((a <loc e) ⇒ (∃b:E. ((¬↑first(b)) c∧ ((a = pred(b) ∈ E) ∧ b ≤loc e ))))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
cand: A c∧ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
cand: A c∧ B,
uimplies: b supposing a,
and: P ∧ Q,
so_apply: x[s],
iff: P ⇐⇒ Q,
or: P ∨ Q,
exists: ∃x:A. B[x],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T}
Latex:
\mforall{}es:EO. \mforall{}e,a:E. ((a <loc e) {}\mRightarrow{} (\mexists{}b:E. ((\mneg{}\muparrow{}first(b)) c\mwedge{} ((a = pred(b)) \mwedge{} b \mleq{}loc e ))))
Date html generated:
2016_05_16-AM-09_23_56
Last ObjectModification:
2015_12_28-PM-09_51_52
Theory : new!event-ordering
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