Nuprl Lemma : es-is-interface-p-first
∀[Info:Type]. ∀es:EO+(Info). ∀[A:Type]. ∀Ias:EClass(A) List. ∀e:E. (↑e ∈b first-eclass(Ias) ⇐⇒ (∃I∈Ias. ↑e ∈b I))
Proof
Definitions occuring in Statement :
first-eclass: first-eclass(Xs),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
l_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: 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,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
top: Top,
so_apply: x[s],
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]. \mforall{}Ias:EClass(A) List. \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-eclass(Ias) \mLeftarrow{}{}\mRightarrow{} (\mexists{}I\mmember{}Ias. \muparrow{}e \mmember{}\msubb{} I))
Date html generated:
2016_05_16-PM-10_56_08
Last ObjectModification:
2015_12_29-AM-10_46_10
Theory : event-ordering
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