Nuprl Lemma : global-eo-info-le-before
∀[L:(Id × Top) List]. ∀[e:E]. (map(λe.info(e);≤loc(e)) ~ map(λx.(snd(x));filter(λx.fst(x) = loc(e);firstn(e + 1;L))))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-info: info(e),
es-le-before: ≤loc(e),
es-loc: loc(e),
es-E: E,
eq_id: a = b,
Id: Id,
filter: filter(P;l),
firstn: firstn(n;as),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
lambda: λx.A[x],
product: x:A × B[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Lemmas :
map_append_sq,
map_cons_lemma,
map_nil_lemma,
global-eo-info-before,
es-E_wf,
global-eo_wf,
top_wf,
event-ordering+_subtype,
list_wf,
Id_wf,
global-eo-E-sq,
firstn_decomp,
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,
le_wf,
decidable__lt,
subtract_wf,
length_wf,
less-iff-le,
trivial-int-eq1,
filter_append_sq,
global-eo-loc,
filter_cons_lemma,
filter_nil_lemma,
eq_id_wf,
select_wf,
bool_wf,
eqtt_to_assert,
assert-eq-id,
global-eo-info,
eqff_to_assert,
eq_id_self,
btrue_wf,
bfalse_wf,
and_wf,
equal_wf,
bnot_wf,
assert_elim,
btrue_neq_bfalse,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not_assert_elim
Latex:
\mforall{}[L:(Id \mtimes{} Top) List]. \mforall{}[e:E].
(map(\mlambda{}e.info(e);\mleq{}loc(e)) \msim{} map(\mlambda{}x.(snd(x));filter(\mlambda{}x.fst(x) = loc(e);firstn(e + 1;L))))
Date html generated:
2015_07_21-PM-04_36_42
Last ObjectModification:
2015_01_27-PM-05_05_21
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