Nuprl Lemma : ranked-eo-info-le-before
∀[L:Id ─→ (Top List)]. ∀[rk:Top]. ∀[e:E]. (map(λe.info(e);≤loc(e)) ~ firstn((snd(e)) + 1;L (fst(e))))
Proof
Definitions occuring in Statement :
ranked-eo: ranked-eo(L;rk),
es-info: info(e),
es-le-before: ≤loc(e),
es-E: E,
Id: Id,
firstn: firstn(n;as),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Lemmas :
top_wf,
Id_wf,
list_wf,
set_wf,
int_seg_wf,
length_wf,
true_wf,
ranked-eo-E-sq,
map_append_sq,
ranked-eo-info-before,
map_cons_lemma,
map_nil_lemma,
ranked-eo-info,
less_than_wf,
squash_wf,
iff_weakening_equal,
lelt_wf,
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,
less-iff-le,
trivial-int-eq1
Latex:
\mforall{}[L:Id {}\mrightarrow{} (Top List)]. \mforall{}[rk:Top]. \mforall{}[e:E].
(map(\mlambda{}e.info(e);\mleq{}loc(e)) \msim{} firstn((snd(e)) + 1;L (fst(e))))
Date html generated:
2015_07_21-PM-04_45_19
Last ObjectModification:
2015_02_04-PM-05_57_19
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