Nuprl Lemma : es-is-le-interface-iff
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. (↑e ∈b le(X) ⇐⇒ (↑e ∈b prior(X)) ∨ (↑e ∈b X))
Proof
Definitions occuring in Statement :
es-le-interface: le(X),
es-prior-interface: prior(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
or: P ∨ Q,
es-le: e ≤loc e' ,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} le(X) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} prior(X)) \mvee{} (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_16-PM-11_53_46
Last ObjectModification:
2015_12_29-AM-01_04_24
Theory : event-ordering
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