Nuprl Lemma : es-pstar-q-partition
∀es:EO. ∀e1,e2,b:E.
∀[Q,P:{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].P[a;b])*[a,b].P[a;b]
⇒ [b;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-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
Lemmas :
exists_wf,
int_seg_wf,
false_wf,
lelt_wf,
es-le_wf,
subtract_wf,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtract-is-less,
all_wf,
es-locl_wf,
decidable__lt,
le-add-cancel2,
sq_stable__le,
es-le-loc,
Id_wf,
es-loc_wf,
es-pstar-q_wf,
es-E_wf,
es-loc-pred,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
es-pred_wf,
lt_int_wf,
bool_wf,
equal-wf-T-base,
less_than_wf,
le_int_wf,
le_wf,
bnot_wf,
zero-le-nat,
subtype_rel_sets,
equal_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
add-mul-special,
zero-mul,
and_wf,
int_subtype_base,
general_arith_equation1,
int_seg_properties,
squash_wf,
not_wf,
member_wf,
es-le-trans2,
es-pred-locl,
iff_weakening_equal,
set_wf
\mforall{}es:EO. \mforall{}e1,e2,b:E.
\mforall{}[Q,P:\{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].P[a;b])*[a,b].P[a;b]
{}\mRightarrow{} [b;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_54_35
Last ObjectModification:
2015_02_04-PM-06_30_06
Home
Index