Nuprl Lemma : once-classrel
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀v:A. uiff(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,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
no-prior-classrel: (no X prior to e),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
alle-lt: ∀e<e'.P[e],
once-class: (X once),
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
cand: A c∧ B,
guard: {T},
rev_implies: P ⇐ Q,
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. uiff(v \mmember{} (X once)(e);(no X prior to e) \mwedge{} v \mmember{} X(e))
Date html generated:
2016_05_16-PM-11_21_35
Last ObjectModification:
2016_01_17-PM-07_12_24
Theory : event-ordering
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