Nuprl Lemma : es-pstar-q_functionality_wrt_rev_implies
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[p',q',p,q:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ {e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ].
((∀a,b:{e:E| loc(e) = loc(e1) ∈ Id} . ((a ∈ [e1, e2]) ⇒ (b ∈ [e1, e2]) ⇒ {p[a;b] ⇐ p'[a;b]}))
⇒ (∀a,b:{e:E| loc(e) = loc(e1) ∈ Id} . ((a ∈ [e1, e2]) ⇒ (b ∈ [e1, e2]) ⇒ {q[a;b] ⇐ q'[a;b]}))
⇒ {[e1;e2]~([a,b].p[a;b])*[a,b].q[a;b] ⇐ [e1;e2]~([a,b].p'[a;b])*[a,b].q'[a;b]})
Proof
Definitions occuring in Statement :
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
es-interval: [e, e'],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[p',q',p,q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}a,b:\{e:E| loc(e) = loc(e1)\} . ((a \mmember{} [e1, e2]) {}\mRightarrow{} (b \mmember{} [e1, e2]) {}\mRightarrow{} \{p[a;b] \mLeftarrow{}{} p'[a;b]\}))
{}\mRightarrow{} (\mforall{}a,b:\{e:E| loc(e) = loc(e1)\} . ((a \mmember{} [e1, e2]) {}\mRightarrow{} (b \mmember{} [e1, e2]) {}\mRightarrow{} \{q[a;b] \mLeftarrow{}{} q'[a;b]\}))
{}\mRightarrow{} \{[e1;e2]\msim{}([a,b].p[a;b])*[a,b].q[a;b] \mLeftarrow{}{} [e1;e2]\msim{}([a,b].p'[a;b])*[a,b].q'[a;b]\})
Date html generated:
2016_05_16-AM-09_55_53
Last ObjectModification:
2015_12_28-PM-09_31_17
Theory : new!event-ordering
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