Nuprl Lemma : single-eclass-val
∀[T:Type]. ∀[A:es:EO+(T) ⟶ E ⟶ Type]. ∀[X:EClass(A[es;e])]. ∀[eo:EO+(T)]. ∀[e:E].
(X eo e) = {X(e)} ∈ bag(A[eo;e]) supposing ↑e ∈b X
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
bag: bag(T)
Definitions unfolded in proof :
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],
all: ∀x:A. B[x],
top: Top,
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ
Latex:
\mforall{}[T:Type]. \mforall{}[A:es:EO+(T) {}\mrightarrow{} E {}\mrightarrow{} Type]. \mforall{}[X:EClass(A[es;e])]. \mforall{}[eo:EO+(T)]. \mforall{}[e:E].
(X eo e) = \{X(e)\} supposing \muparrow{}e \mmember{}\msubb{} X
Date html generated:
2016_05_16-PM-02_19_28
Last ObjectModification:
2015_12_29-AM-11_44_49
Theory : event-ordering
Home
Index