Nuprl Lemma : es-pred_property
∀es:EO. ∀e:E.
{(loc(pred(e)) = loc(e) ∈ Id)
∧ (pred(e) < e)
∧ (∀e':E. (e' < e) ⇒ ((e' = pred(e) ∈ E) ∨ (e' < pred(e))) supposing loc(e') = loc(e) ∈ Id)}
supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-first: first(e),
es-pred: pred(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
es-pred_property_base,
assert_wf,
es-first_wf,
es-E_wf,
not_wf,
event_ordering_wf,
assert-es-eq-E-base,
es-eq-E-wf-base,
es-pred-wf-base,
bool_wf,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
btrue_wf,
true_wf,
es-causl_wf,
es-pred_wf,
equal_wf,
Id_wf,
es-loc_wf,
es-dom_wf,
sq_stable__assert
\mforall{}es:EO. \mforall{}e:E.
\{(loc(pred(e)) = loc(e))
\mwedge{} (pred(e) < e)
\mwedge{} (\mforall{}e':E. (e' < e) {}\mRightarrow{} ((e' = pred(e)) \mvee{} (e' < pred(e))) supposing loc(e') = loc(e))\}
supposing \mneg{}\muparrow{}first(e)
Date html generated:
2015_07_17-AM-08_35_27
Last ObjectModification:
2015_01_27-PM-02_58_41
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