Nuprl Lemma : es-pplus-trivial
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[Q:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ {e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ]
(e1 ≤loc e2 ⇒ Q[e1;e2] ⇒ [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-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 :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
(e1 \mleq{}loc e2 {}\mRightarrow{} Q[e1;e2] {}\mRightarrow{} [e1,e2]\msim{}([a,b].Q[a;b])+)
Date html generated:
2016_05_16-AM-09_57_31
Last ObjectModification:
2015_12_28-PM-09_30_24
Theory : new!event-ordering
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