Nuprl Lemma : eo-forward-before
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e,b:E]. before(e) = filter(λa.b ≤loc a;before(e)) ∈ (E List) supposing b ≤loc e
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-before: before(e),
es-ble: e ≤loc e',
es-le: e ≤loc e' ,
es-E: E,
filter: filter(P;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-le_wf,
event-ordering+_subtype,
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,
eo-forward-first,
member-eo-forward-E,
Id_wf,
es-loc_wf,
eo-forward-loc,
eq_id_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert-eq-id,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
es-first_wf2,
filter_is_nil,
es-ble_wf,
es-before_wf,
es-le-loc,
nil_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-eq-E_wf,
assert-es-eq-E-2,
l_all_iff,
l_member_wf,
member-es-before,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
assert-es-ble,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-pred-causl,
es-le-pred,
es-le_weakening,
eo-forward-pred,
iff_weakening_equal,
eo-forward_wf,
filter_nil_lemma,
filter_append_sq,
append_wf,
list_wf,
es-before_wf3,
subtype_rel_list,
es-locl_wf,
subtype_rel_set,
eo-forward-E-subtype,
filter_cons_lemma,
and_wf,
cons_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e,b:E].
before(e) = filter(\mlambda{}a.b \mleq{}loc a;before(e)) supposing b \mleq{}loc e
Date html generated:
2015_07_17-PM-00_05_27
Last ObjectModification:
2015_02_04-PM-05_42_35
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