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
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
es-pplus: [e1,e2]~([a,b].p[a; b])+,
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-locl: (e <loc e'),
and: P ∧ Q,
not: ¬A,
false: False
Latex:
\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:
2016_05_16-AM-09_58_36
Last ObjectModification:
2015_12_28-PM-09_30_51
Theory : new!event-ordering
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