Nuprl Lemma : iseg-es-le-before-is-before
∀[es:EO]. ∀[e,x:E]. ∀[L:E List]. L = before(x) ∈ (E List) supposing L @ [x] ≤ ≤loc(e)
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-before: before(e),
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Lemmas :
length_wf_nat,
Id_wf,
es-loc_wf,
es-le-before_wf,
equal_wf,
nat_wf,
member_append,
member_singleton,
l_member_wf,
member-es-le-before,
es-le-before-partition,
exists_wf,
append_wf,
es-before_wf,
append_assoc,
es-le-before-no_repeats,
no_repeats_wf,
list-decomp-no_repeats,
iseg_wf,
es-E_wf,
cons_wf,
nil_wf,
es-le-before_wf2,
subtype_rel_list,
es-le_wf,
list_wf,
event_ordering_wf,
es-bless_wf,
bool_wf,
eqtt_to_assert,
assert-es-bless,
list_ind_cons_lemma,
list_ind_nil_lemma,
es-open-interval_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-locl_wf,
es-locl-trichotomy,
es-le-loc,
es-locl_transitivity1,
es-locl_transitivity2,
decidable__assert,
es-first_wf2,
not_wf,
assert_wf,
es-pred_wf,
es-pred-locl,
es-le_weakening,
squash_wf,
true_wf,
es-interval-open-interval,
iff_weakening_equal,
es-open-interval-nil
\mforall{}[es:EO]. \mforall{}[e,x:E]. \mforall{}[L:E List]. L = before(x) supposing L @ [x] \mleq{} \mleq{}loc(e)
Date html generated:
2015_07_17-AM-08_44_35
Last ObjectModification:
2015_02_04-AM-07_09_30
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