Nuprl Lemma : es-le-before-filter
∀es:EO. ∀e,b:E. (b ≤loc e ⇒ (≤loc(b) = filter(λa.a ≤loc b;≤loc(e)) ∈ ({a:E| a ≤loc b } List)))
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-ble: e ≤loc e',
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
filter: filter(P;l),
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
lambda: λx.A[x],
equal: s = t ∈ T
Lemmas :
es-le_wf,
es-E_wf,
event_ordering_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-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,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-le-iff,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
es-le-before-pred,
squash_wf,
true_wf,
filter_append_sq,
filter_cons_lemma,
filter_nil_lemma,
es-ble_wf,
bool_wf,
eqtt_to_assert,
assert-es-ble,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
append_back_nil,
list_wf,
iff_weakening_equal,
es-le_transitivity,
es-locl_transitivity2,
es-locl_irreflexivity,
es-le-before_wf2,
subtype_rel_list,
filter_wf5,
l_member_wf,
filter_trivial,
Id_wf,
es-loc_wf,
es-le-before_wf,
l_all_iff,
set_wf,
assert_wf,
member-es-le-before2,
filter_type,
subtype_rel_list_set,
list_set_type,
length_wf_nat,
l_all_wf2
\mforall{}es:EO. \mforall{}e,b:E. (b \mleq{}loc e {}\mRightarrow{} (\mleq{}loc(b) = filter(\mlambda{}a.a \mleq{}loc b;\mleq{}loc(e))))
Date html generated:
2015_07_17-AM-08_43_05
Last ObjectModification:
2015_02_04-AM-07_09_16
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