Nuprl Lemma : once-classrel-weak
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀v:A. (v ∈ (X once)(e) ⇐⇒ (no X prior to e) ∧ v ∈ {X}(e))
Proof
Definitions occuring in Statement :
once-class: (X once),
no-prior-classrel: (no X prior to e),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}v:A. (v \mmember{} (X once)(e) \mLeftarrow{}{}\mRightarrow{} (no X prior to e) \mwedge{} v \mmember{} \{X\}(e))
Date html generated:
2016_05_16-PM-11_21_49
Last ObjectModification:
2015_12_29-AM-10_24_07
Theory : event-ordering
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