Nuprl Lemma : es-pplus-partition
∀es:EO. ∀e1,e2,b:E.
∀[Q:{e:E| loc(e) = loc(e1) ∈ Id} ─→ {e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ]
((e1 <loc b) ⇒ b ≤loc e2 ⇒ [e1,pred(b)]~([a,b].Q[a;b])+ ⇒ [b,e2]~([a,b].Q[a;b])+ ⇒ [e1,e2]~([a,b].Q[a;b])+)
Proof
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-pplus_wf,
es-le-loc,
Id_wf,
es-loc_wf,
es-E_wf,
es-loc-pred,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
es-pred_wf,
es-le_wf,
es-locl_wf,
es-pstar-q-partition
\mforall{}es:EO. \mforall{}e1,e2,b:E.
\mforall{}[Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
((e1 <loc b)
{}\mRightarrow{} b \mleq{}loc e2
{}\mRightarrow{} [e1,pred(b)]\msim{}([a,b].Q[a;b])+
{}\mRightarrow{} [b,e2]\msim{}([a,b].Q[a;b])+
{}\mRightarrow{} [e1,e2]\msim{}([a,b].Q[a;b])+)
Date html generated:
2015_07_17-AM-08_55_15
Last ObjectModification:
2015_01_27-PM-01_04_43
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