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
Lemmas :
rec_select_update_lemma,
assert_wf,
bool_wf,
event_ordering_wf,
eo-reset-dom-reset-dom,
es-dom_wf,
eqtt_to_assert,
es-base-E_wf,
band_assoc,
eo-reset-dom_wf,
iff_weakening_equal
\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:
2015_07_17-AM-08_34_32
Last ObjectModification:
2015_02_04-AM-07_07_24
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