Nuprl Lemma : es-is-prior-interface-pred
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. (↑e ∈b prior(X) ⇐⇒ (¬↑first(e)) ∧ ((↑pred(e) ∈b X) ∨ (↑pred(e) ∈b prior(X))))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
cand: A c∧ B
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} prior(X) \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e)) \mwedge{} ((\muparrow{}pred(e) \mmember{}\msubb{} X) \mvee{} (\muparrow{}pred(e) \mmember{}\msubb{} prior(X))))
Date html generated:
2016_05_16-PM-11_53_04
Last ObjectModification:
2015_12_29-AM-01_05_38
Theory : event-ordering
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