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
Lemmas :
bool_cases_sqequal,
es-dom_wf,
assert_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
es-base-E_wf
\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:
2015_07_17-AM-08_34_32
Last ObjectModification:
2015_01_27-PM-03_00_52
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