Nuprl Lemma : es-interface-history-first
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E].
es-interface-history(es;X;e) = if e ∈b X then X(e) else [] fi ∈ (A List) supposing ↑first(e)
Proof
Definitions occuring in Statement :
es-interface-history: es-interface-history(es;X;e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-E: E,
nil: [],
list: T List,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
es-interface-history: es-interface-history(es;X;e),
es-le-before: ≤loc(e),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-before: before(e),
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],
not: ¬A,
implies: P ⇒ Q,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mapfilter: mapfilter(f;P;L),
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
map: map(f;as),
nil: []
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A List)]. \mforall{}[e:E].
es-interface-history(es;X;e) = if e \mmember{}\msubb{} X then X(e) else [] fi supposing \muparrow{}first(e)
Date html generated:
2016_05_16-PM-10_57_31
Last ObjectModification:
2015_12_29-AM-10_43_49
Theory : event-ordering
Home
Index