Nuprl Lemma : until-classrel
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A].
(v ∈ (X until Y)(e) ⇐⇒ (no Y prior to e) ∧ v ∈ X(e))
Proof
Definitions occuring in Statement :
until-class: (X until Y),
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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
no-prior-classrel: (no X prior to e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
alle-lt: ∀e<e'.P[e],
not: ¬A,
false: False,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
rev_implies: P ⇐ Q,
until-class: (X until Y),
or: P ∨ Q,
existse-before: ∃e<e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
eclass: EClass(A[eo; e]),
true: True,
guard: {T}
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A].
(v \mmember{} (X until Y)(e) \mLeftarrow{}{}\mRightarrow{} (no Y prior to e) \mwedge{} v \mmember{} X(e))
Date html generated:
2016_05_16-PM-11_20_21
Last ObjectModification:
2016_01_17-PM-07_13_19
Theory : event-ordering
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