Nuprl Lemma : send-once-classrel
∀[Info,A:Type]. ∀[b:bag(A)]. ∀es:EO+(Info). ∀e:E. ∀v:A. (v ∈ Send(b)(e) ⇐⇒ v ↓∈ b ∧ (↑first(e)))
Proof
Definitions occuring in Statement :
send-once-class: Send(b),
classrel: v ∈ X(e),
event-ordering+: EO+(Info),
es-first: first(e),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
send-once-class: Send(b),
classrel: v ∈ X(e),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
eclass: EClass(A[eo; e]),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
no-prior-classrel: (no X prior to e),
alle-lt: ∀e<e'.P[e],
not: ¬A,
false: False,
uiff: uiff(P;Q),
bag-member: x ↓∈ bs,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q
Latex:
\mforall{}[Info,A:Type]. \mforall{}[b:bag(A)]. \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:A. (v \mmember{} Send(b)(e) \mLeftarrow{}{}\mRightarrow{} v \mdownarrow{}\mmember{} b \mwedge{} (\muparrow{}first(e)))
Date html generated:
2016_05_16-PM-11_23_10
Last ObjectModification:
2016_01_17-PM-07_11_52
Theory : event-ordering
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