Nuprl Lemma : es-interval-open-interval
∀[es:EO]. ∀[e,e':E]. [e', e] = (if e' <loc e then [e'] else [] fi @ (e', e) @ [e]) ∈ (E List) supposing e' ≤loc e
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-interval: [e, e'],
es-bless: e <loc e',
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[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-first_wf2,
bool_wf,
eqtt_to_assert,
list_ind_nil_lemma,
filter_nil_lemma,
filter_cons_lemma,
es-ble_wf,
assert-es-ble,
es-bless_wf,
assert-es-bless,
list_ind_cons_lemma,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-locl_wf,
cons_wf,
nil_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
assert_of_bnot,
filter_append_sq,
iff_transitivity,
iff_weakening_uiff,
append_assoc_sq,
append_wf,
es-le-iff,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-pred_wf,
and_wf,
ifthenelse_wf,
es-le-first,
es-pred-locl,
es-causl_weakening,
es-le-pred,
length_wf_nat,
filter_wf5,
es-before_wf,
l_member_wf,
list_wf,
filter_is_nil,
l_all_iff,
member_append,
member-es-before,
member_singleton,
or_wf,
es-locl_transitivity1,
es-le_weakening,
es-le_transitivity,
squash_wf,
true_wf,
es-le-before_wf2,
subtype_rel_list,
member-es-le-before
\mforall{}[es:EO]. \mforall{}[e,e':E].
[e', e] = (if e' <loc e then [e'] else [] fi @ (e', e) @ [e]) supposing e' \mleq{}loc e
Date html generated:
2015_07_17-AM-08_42_53
Last ObjectModification:
2015_01_27-PM-02_43_30
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