Nuprl Lemma : es-pred_property_base
∀es:EO. ∀e:es-base-E(es).
((loc(pred(e)) = loc(e) ∈ Id)
∧ ((pred(e) < e) ∨ (pred(e) = e ∈ es-base-E(es)))
∧ (∀e':E. (e' < e) ⇒ ((e' = pred(e) ∈ es-base-E(es)) ∨ (e' < pred(e))) supposing loc(e') = loc(e) ∈ Id))
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
es-pred-wf-base,
decidable__equal-es-base-E,
es-causl-wf-base,
es-pred-less-base,
equal_wf,
es-base-E_wf,
es-loc-wf-base,
Id_wf,
es-loc_wf,
es-E_wf,
decidable__es-causl-same-loc,
es-pred-loc-base,
iff_weakening_equal,
es-pred-maximal-base,
es-causl-total-base
\mforall{}es:EO. \mforall{}e:es-base-E(es).
((loc(pred(e)) = loc(e))
\mwedge{} ((pred(e) < e) \mvee{} (pred(e) = e))
\mwedge{} (\mforall{}e':E. (e' < e) {}\mRightarrow{} ((e' = pred(e)) \mvee{} (e' < pred(e))) supposing loc(e') = loc(e)))
Date html generated:
2015_07_17-AM-08_35_23
Last ObjectModification:
2015_02_04-AM-07_07_22
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