Nuprl Lemma : pred-hd-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. pred(hd((e1, e2))) = e1 ∈ E supposing ||(e1, e2)|| > 0
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
hd: hd(l),
length: ||as||,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
gt: i > j,
natural_number: $n,
equal: s = t ∈ T
Lemmas :
member-es-open-interval,
hd_wf,
decidable__le,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-associates,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
hd_member,
list_wf,
es-E_wf,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
gt_wf,
length_wf,
es-pred_property,
assert_elim,
es-first_wf2,
es-locl-first,
btrue_neq_bfalse,
assert_wf,
es-causl_weakening,
es-open-interval_wf,
event_ordering_wf,
member_filter_2,
es-before_wf,
l_member_wf,
es-bless_wf,
es-pred_wf,
member-es-before,
es-pred-locl,
es-loc-pred,
subtype_base_sq,
bool_subtype_base,
bool_wf,
es-causl_transitivity2,
assert_of_ff,
es-causle_weakening_locl,
es-le_weakening,
assert-es-bless,
es-locl_wf,
select0,
es-le_wf,
es-causl_irreflexivity,
decidable__equal_int,
int_subtype_base,
es-le-self,
select_wf,
es-open-interval-ordered,
int_seg_subtype-nat,
zero-le-nat,
length_wf_nat,
length_cons,
length_wf_nil,
non_neg_length,
length_nil,
nil_wf,
cons_wf,
all_wf,
subtype_rel_dep_function,
increasing_wf,
minus-zero,
decidable__lt,
le_antisymmetry_iff,
int_seg_wf,
le-add-cancel,
not-equal-2,
not-le-2,
neg_assert_of_eq_int,
assert-bnot,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
lelt_wf,
nequal-le-implies,
nat_properties,
le_wf,
int_upper_subtype_nat,
assert_of_eq_int,
eqtt_to_assert,
eq_int_wf,
sq_stable__le
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. pred(hd((e1, e2))) = e1 supposing ||(e1, e2)|| > 0
Date html generated:
2015_07_17-AM-08_43_48
Last ObjectModification:
2015_07_16-AM-09_51_46
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