Nuprl Lemma : is-prior-val
∀[Info:Type]. ∀es:EO+(Info). ∀[T:Type]. ∀X:EClass(T). ∀e:E. (↑e ∈b (X)' ⇐⇒ ∃e':E. ((e' <loc e) ∧ (↑e' ∈b X)))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-prior-val: (X)',
in-eclass: e ∈b X,
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
assert: ↑b,
iff: P ⇐⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
not: ¬A
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}[T:Type]. \mforall{}X:EClass(T). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} (X)' \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. ((e' <loc e) \mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)))
Date html generated:
2016_05_17-AM-06_32_54
Last ObjectModification:
2015_12_29-AM-00_33_55
Theory : event-ordering
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