Nuprl Lemma : is-prior-interface
∀[Info:Type]. ∀X:EClass(Top). ∀es:EO+(Info). ∀e:E. (↑e ∈b prior(X) ⇐⇒ ∃e':E. ((e' <loc e) ∧ (↑e' ∈b 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-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-prior-interface: prior(X),
member: t ∈ T,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
in-eclass: e ∈b X,
local-pred-class: local-pred-class(P),
and: P ∧ Q,
can-apply: can-apply(f;x),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
or: P ∨ Q,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
eq_int: (i =z j),
bfalse: ff,
sq_exists: ∃x:{A| B[x]},
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]
\mforall{}X:EClass(Top). \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} prior(X) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. ((e' <loc e) \mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)))
Date html generated:
2016_05_16-PM-11_50_40
Last ObjectModification:
2015_12_29-AM-10_05_59
Theory : event-ordering
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