Nuprl Lemma : eo-restrict-restrict
∀[es:EO]. ∀[P:E ⟶ 𝔹]. ∀[Q:{e:E| ↑(P e)} ⟶ 𝔹].
(eo-restrict(eo-restrict(es;P);Q) = eo-restrict(es;λe.((P e) ∧b (Q e))) ∈ EO)
Proof
Definitions occuring in Statement :
eo-restrict: eo-restrict(eo;P),
es-E: E,
event_ordering: EO,
band: p ∧b q,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eo-restrict: eo-restrict(eo;P),
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
prop: ℙ,
es-dom: es-dom(es),
es-E: E,
es-base-E: es-base-E(es),
eo-reset-dom: eo-reset-dom(es;d),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
band: p ∧b q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[es:EO]. \mforall{}[P:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[Q:\{e:E| \muparrow{}(P e)\} {}\mrightarrow{} \mBbbB{}].
(eo-restrict(eo-restrict(es;P);Q) = eo-restrict(es;\mlambda{}e.((P e) \mwedge{}\msubb{} (Q e))))
Date html generated:
2016_05_16-AM-09_14_53
Last ObjectModification:
2015_12_28-PM-09_57_41
Theory : new!event-ordering
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