Nuprl Lemma : ranked-eo-property
∀[Info:Type]
∀L:Id ─→ (Info List)
∀[rk:(i:Id × ℕ||L i||) ─→ ℕ]
∀i:Id. (0 < ||L i|| ⇒ (∃e:E. ((L i) = map(λe.info(e);≤loc(e)) ∈ (Info List))))
supposing ∀i:Id. ∀j:ℕ||L i||. ∀k:ℕj. rk <i, k> < rk <i, j>
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,
map: map(f;as),
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Lemmas :
member-less_than,
less_than_transitivity2,
length_wf,
le_weakening2,
lelt_wf,
int_seg_wf,
nat_wf,
Id_wf,
ranked-eo-E,
subtype_rel_dep_function,
list_wf,
top_wf,
subtype_rel_list,
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,
subtract-is-less,
ranked-eo-info-le-before,
firstn_all,
add-mul-special,
zero-mul,
equal_wf,
map_wf,
es-E_wf,
ranked-eo_wf,
event-ordering+_subtype,
es-loc_wf,
es-info_wf,
es-le-before_wf,
less_than_wf,
all_wf
Latex:
\mforall{}[Info:Type]
\mforall{}L:Id {}\mrightarrow{} (Info List)
\mforall{}[rk:(i:Id \mtimes{} \mBbbN{}||L i||) {}\mrightarrow{} \mBbbN{}]
\mforall{}i:Id. (0 < ||L i|| {}\mRightarrow{} (\mexists{}e:E. ((L i) = map(\mlambda{}e.info(e);\mleq{}loc(e)))))
supposing \mforall{}i:Id. \mforall{}j:\mBbbN{}||L i||. \mforall{}k:\mBbbN{}j. rk <i, k> < rk <i, j>
Date html generated:
2015_07_21-PM-04_45_34
Last ObjectModification:
2015_01_27-PM-04_58_36
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