Nuprl Lemma : es-pstar-q_functionality_wrt_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],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-pstar-q_wf,
decidable__lt,
false_wf,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
lelt_wf,
decidable__le,
not-le-2,
sq_stable__le,
zero-add,
add-zero,
le-add-cancel,
es-loc-pred,
assert_elim,
es-first_wf2,
es-locl-first,
btrue_neq_bfalse,
assert_wf,
es-pred_wf,
Id_wf,
es-loc_wf,
es-locl_wf,
equal_wf,
int_seg_wf,
subtract_wf,
minus-minus,
subtract-is-less,
es-le_wf,
all_wf,
exists_wf,
es-E_wf,
l_member_wf,
es-interval_wf,
set_wf,
event_ordering_wf,
es-increasing-sequence2,
subtype_rel_dep_function,
less_than_transitivity2,
le_weakening2,
member-es-interval,
squash_wf,
true_wf,
iff_weakening_equal,
es-le_transitivity,
es-le-pred,
es-le_weakening_eq,
es-locl_transitivity1,
es-pred-locl,
es-locl_transitivity2,
subtype_base_sq,
bool_subtype_base,
bool_wf,
es-le-self
\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] {}\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] {}\mRightarrow{} q'[a;b]\}))
{}\mRightarrow{} \{[e1;e2]\msim{}([a,b].p[a;b])*[a,b].q[a;b] {}\mRightarrow{} [e1;e2]\msim{}([a,b].p'[a;b])*[a,b].q'[a;b]\})
Date html generated:
2015_07_17-AM-08_53_50
Last ObjectModification:
2015_02_04-PM-06_30_18
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