Nuprl Lemma : es-interface-predecessors-nil
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(pred(e)) ~ []) supposing ((¬↑first(e)) and (¬↑e ∈b prior(X)))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
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,
nil: [],
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
es-E-interface: E(X),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
or: P ∨ Q,
cons: [a / b],
not: ¬A,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
es-interface-predecessors: ≤(X)(e),
guard: {T},
exists: ∃x:A. B[x],
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(pred(e)) \msim{} []) supposing ((\mneg{}\muparrow{}first(e)) and (\mneg{}\muparrow{}e \mmember{}\msubb{} prior(X)))
Date html generated:
2016_05_16-PM-11_51_49
Last ObjectModification:
2015_12_29-AM-10_07_34
Theory : event-ordering
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