Nuprl Lemma : ranked-lists-to-extended-eo
∀[Info:Type]
∀L:Id ─→ (Info List). ∀rk:(i:Id × ℕ||L i||) ─→ ℕ.
∃es:EO+(Info). ∀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 :
es-info: info(e),
event-ordering+: EO+(Info),
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_wf,
ranked-eo-property,
all_wf,
less_than_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
equal_wf,
list_wf,
map_wf,
es-loc_wf,
es-info_wf,
es-le-before_wf
Latex:
\mforall{}[Info:Type]
\mforall{}L:Id {}\mrightarrow{} (Info List). \mforall{}rk:(i:Id \mtimes{} \mBbbN{}||L i||) {}\mrightarrow{} \mBbbN{}.
\mexists{}es:EO+(Info). \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_51
Last ObjectModification:
2015_01_27-PM-04_58_19
Home
Index