Nuprl Lemma : prior-vals-non-null
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E(X)]. (¬↑null(X(≤e)))
Proof
Definitions occuring in Statement :
es-interface-prior-vals: X(≤e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
null: null(as),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
es-interface-prior-vals: X(≤e),
prop: ℙ,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)]. (\mneg{}\muparrow{}null(X(\mleq{}e)))
Date html generated:
2016_05_16-PM-11_04_37
Last ObjectModification:
2015_12_29-AM-10_38_32
Theory : event-ordering
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