Nuprl Lemma : global-eo-first
∀[L:(Id × Top) List]. ∀[e:E]. (first(e) ~ (∀x∈upto(e).¬bloc(x) = loc(e))_b)
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-first: first(e),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
Id: Id,
bl-all: (∀x∈L.P[x])_b,
upto: upto(n),
list: T List,
bnot: ¬bb,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Lemmas :
es-E_wf,
global-eo_wf,
top_wf,
event-ordering+_subtype,
list_wf,
Id_wf,
global-eo-E-sq,
global-eo-loc,
global-eo-E,
subtype_rel_list,
es-pred-wf-base,
subtype_rel_self,
lelt_wf,
length_wf,
global-eo-base-E,
true_wf,
global-eo-eq-E,
global-eo-dom,
rec_select_update_lemma,
select_wf,
int_seg_wf,
sq_stable__le,
value-type-has-value,
atom2-value-type,
firstn_wf,
set-value-type,
int-value-type,
last_index_wf,
eq_id_wf,
last_index_property,
length_firstn,
subtype_rel_sets,
le_wf,
le_weakening2,
less_than_wf,
assert_wf,
subtract_wf,
decidable__le,
false_wf,
not-le-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,
not_wf,
l_exists_wf,
nth_tl_wf,
l_member_wf,
equal-wf-T-base,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bl-all_wf,
upto_wf,
bnot_wf,
less_than_transitivity2,
assert-bl-all,
length_upto,
int_seg_subtype-nat,
zero-le-nat,
nat_wf,
non_neg_length,
length_firstn_eq,
length_wf_nat,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-eq-id,
assert_functionality_wrt_uiff,
squash_wf,
pi1_wf_top,
select_upto,
select_firstn,
iff_weakening_equal,
decidable__lt,
not-equal-2,
minus-zero,
le_antisymmetry_iff,
subtype_rel_nested_set,
set_wf,
l_all_wf2,
subtype_rel_nested_set2,
select-firstn,
assert_elim,
bfalse_wf,
and_wf,
btrue_neq_bfalse,
bool_sq
Latex:
\mforall{}[L:(Id \mtimes{} Top) List]. \mforall{}[e:E]. (first(e) \msim{} (\mforall{}x\mmember{}upto(e).\mneg{}\msubb{}loc(x) = loc(e))\_b)
Date html generated:
2015_07_21-PM-04_35_43
Last ObjectModification:
2015_02_04-PM-06_00_16
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