Nuprl Lemma : es-pstar-q_functionality_wrt_iff
∀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,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-pstar-q_wf,
all_wf,
es-E_wf,
Id_wf,
es-loc_wf,
l_member_wf,
es-interval_wf,
iff_wf,
set_wf,
event_ordering_wf,
es-pstar-q_functionality_wrt_rev_implies,
iff_weakening_equal
\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{}{}\mRightarrow{} 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{}{}\mRightarrow{} q'[a;b])))
{}\mRightarrow{} ([e1;e2]\msim{}([a,b].p[a;b])*[a,b].q[a;b] \mLeftarrow{}{}\mRightarrow{} [e1;e2]\msim{}([a,b].p'[a;b])*[a,b].q'[a;b]))
Date html generated:
2015_07_17-AM-08_54_03
Last ObjectModification:
2015_02_04-PM-06_27_54
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