Nuprl Lemma : ranked-eo-before
∀[L:Id ─→ (Top List)]. ∀[rk:Top]. ∀[e:E]. (before(e) ~ map(λn.<fst(e), n>;upto(snd(e))))
Proof
Definitions occuring in Statement :
ranked-eo: ranked-eo(L;rk),
es-before: before(e),
es-E: E,
Id: Id,
upto: upto(n),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
lambda: λx.A[x],
function: x:A ─→ B[x],
pair: <a, b>,
sqequal: s ~ t
Lemmas :
ranked-eo-E-sq,
int_seg_subtype-nat,
false_wf,
nat_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
decidable__le,
subtract_wf,
not-ge-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,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
lelt_wf,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
set_wf,
Id_wf,
length_wf,
top_wf,
true_wf,
list_wf,
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,
int_upper_subtype_nat,
nequal-le-implies,
ranked-eo-first,
ranked-eo-pred,
int_subtype_base,
list_subtype_base,
product_subtype_base,
atom2_subtype_base,
set_subtype_base,
map_wf,
nil_wf,
subtract-is-less,
upto_decomp1,
map_append_sq,
map_cons_lemma,
map_nil_lemma
Latex:
\mforall{}[L:Id {}\mrightarrow{} (Top List)]. \mforall{}[rk:Top]. \mforall{}[e:E]. (before(e) \msim{} map(\mlambda{}n.<fst(e), n>upto(snd(e))))
Date html generated:
2015_07_21-PM-04_44_51
Last ObjectModification:
2015_01_27-PM-05_04_29
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