Nuprl Lemma : prior-val-all-events
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. prior(E)(e) = pred(e) ∈ E supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-all-events: E,
eclass-val: X(e),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
es-all-events: E,
local-pred-class: local-pred-class(P),
all: ∀x:A. B[x],
top: Top,
eq_int: (i =z j),
es-local-pred: last(P),
ifthenelse: if b then t else f fi ,
btrue: tt,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. prior(E)(e) = pred(e) supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_17-AM-06_41_24
Last ObjectModification:
2015_12_29-AM-00_27_51
Theory : event-ordering
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