Nuprl Lemma : eo-restrict_property
∀es:EO. ∀P:E ⟶ 𝔹. (E ≡ {e:E| ↑(P e)} ∧ (∀e:E. (loc(e) = loc(e) ∈ Id)) ∧ (∀e1,e2:E. ((e1 < e2) ⇐⇒ (e1 < e2))))
Proof
Definitions occuring in Statement :
es-causl: (e < e'),
es-loc: loc(e),
eo-restrict: eo-restrict(eo;P),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
bool: 𝔹,
ext-eq: A ≡ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
es-E: E,
eo-restrict: eo-restrict(eo;P),
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
es-loc: loc(e),
record-select: r.x,
record-update: r[x := v],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
es-causl: (e < e'),
rev_implies: P ⇐ Q,
es-dom: es-dom(es),
es-base-E: es-base-E(es),
ext-eq: A ≡ B,
or: P ∨ Q,
band: p ∧b q,
assert: ↑b,
true: True,
false: False,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb
Latex:
\mforall{}es:EO. \mforall{}P:E {}\mrightarrow{} \mBbbB{}.
(E \mequiv{} \{e:E| \muparrow{}(P e)\} \mwedge{} (\mforall{}e:E. (loc(e) = loc(e))) \mwedge{} (\mforall{}e1,e2:E. ((e1 < e2) \mLeftarrow{}{}\mRightarrow{} (e1 < e2))))
Date html generated:
2016_05_16-AM-09_14_51
Last ObjectModification:
2015_12_28-PM-09_59_09
Theory : new!event-ordering
Home
Index