Nuprl Lemma : embedding-preserves-local-class
∀[Info,A:Type]. ∀[X:EClass(A)].
(LocalClass(X)
⇒ (∀eo1,eo2:EO+(Info). ∀f:E ⟶ E.
(es-local-embedding(Info;eo1;eo2;f) ⇒ (∀[e:E]. ∀[v:A]. (v ∈ X(e) ⇐⇒ v ∈ X(f e))))))
Proof
Definitions occuring in Statement :
local-class: LocalClass(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
classrel: v ∈ X(e),
class-ap: X(e),
squash: ↓T,
prop: ℙ,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
es-le-before: ≤loc(e),
top: Top,
subtype_rel: A ⊆r B,
or: P ∨ Q,
length: ||as||,
list_ind: list_ind,
map: map(f;as),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
ge: i ≥ j ,
bag-member: x ↓∈ bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)].
(LocalClass(X)
{}\mRightarrow{} (\mforall{}eo1,eo2:EO+(Info). \mforall{}f:E {}\mrightarrow{} E.
(es-local-embedding(Info;eo1;eo2;f) {}\mRightarrow{} (\mforall{}[e:E]. \mforall{}[v:A]. (v \mmember{} X(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} X(f e))))))
Date html generated:
2016_05_16-PM-02_05_38
Last ObjectModification:
2016_01_17-PM-07_42_37
Theory : event-ordering
Home
Index