Nuprl Lemma : es-prior-interface-vals-nil
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[e:E]. uiff(X(<e) = [] ∈ (A List);¬↑e ∈b prior(X))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-prior-interface-vals: X(<e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
nil: [],
list: T List,
assert: ↑b,
uiff: uiff(P;Q),
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,
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,
implies: P ⇒ Q,
sq_stable: SqStable(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
not: ¬A,
false: False,
prop: ℙ,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
squash: ↓T,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[e:E]. uiff(X(<e) = [];\mneg{}\muparrow{}e \mmember{}\msubb{} prior(X))
Date html generated:
2016_05_17-AM-06_28_42
Last ObjectModification:
2016_01_17-PM-06_42_20
Theory : event-ordering
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