Nuprl Lemma : iseg-global-order-history
∀[Info:Type]
∀L1,L2:(Id × Info) List. (L1 ≤ L2 ⇒ (∀e:E. (map(λx.info(x);≤loc(e)) = map(λx.info(x);≤loc(e)) ∈ Info List+)))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-info: info(e),
es-le-before: ≤loc(e),
es-E: E,
Id: Id,
iseg: l1 ≤ l2,
listp: A List+,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
iseg_length,
iseg-global-order-loc,
es-E_wf,
global-eo_wf,
event-ordering+_subtype,
iseg_wf,
list_wf,
Id_wf,
global-eo-info-le-before,
subtype_rel_list,
top_wf,
subtype_rel_product,
global-eo-E-sq,
global-eo-E,
less_than_transitivity1,
length_wf,
lelt_wf,
subtype_base_sq,
atom2_subtype_base,
eq_id_wf,
bool_wf,
map_wf_listp,
squash_wf,
true_wf,
listp_wf,
filter_wf5,
set_wf,
l_member_wf,
subtype_rel_dep_function,
firstn_wf,
subtype_rel_self,
length_wf_nat,
equal_wf,
nat_wf,
firstn_append,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
sq_stable__le,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
less-iff-le,
le-add-cancel2,
assert_of_lt_int,
length-filter-pos,
non_neg_length,
length_firstn_eq,
le_wf,
assert_wf,
select_wf,
select-firstn,
add-mul-special,
zero-mul,
assert-eq-id,
global-eo-loc,
lt_int_wf
Latex:
\mforall{}[Info:Type]
\mforall{}L1,L2:(Id \mtimes{} Info) List. (L1 \mleq{} L2 {}\mRightarrow{} (\mforall{}e:E. (map(\mlambda{}x.info(x);\mleq{}loc(e)) = map(\mlambda{}x.info(x);\mleq{}loc(e)))))
Date html generated:
2015_07_21-PM-04_37_48
Last ObjectModification:
2015_01_27-PM-05_09_19
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