Nuprl Lemma : ranked-eo-locl
∀[L:Id ─→ (Top List)]. ∀[rk:(i:Id × ℕ||L i||) ─→ ℕ].
∀[a,b:E]. uiff((a <loc b);((fst(a)) = (fst(b)) ∈ Id) ∧ snd(a) < snd(b))
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-locl: (e <loc e'),
es-E: E,
Id: Id,
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
equal: s = t ∈ T
Lemmas :
ranked-eo-E-sq,
rec_select_update_lemma,
member-less_than,
squash_wf,
less_than_wf,
int_seg_wf,
length_wf,
subtype_base_sq,
Id_wf,
atom2_subtype_base,
lelt_wf,
top_wf,
subtype_rel_self,
es-locl_wf,
ranked-eo_wf,
event-ordering+_subtype,
es-E_wf,
all_wf,
less_than_transitivity2,
le_weakening2,
nat_wf,
list_wf,
and_wf,
equal_wf,
decidable__lt,
int_subtype_base,
less_than_irreflexivity,
false_wf,
not-equal-2,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
add-associates
Latex:
\mforall{}[L:Id {}\mrightarrow{} (Top List)]. \mforall{}[rk:(i:Id \mtimes{} \mBbbN{}||L i||) {}\mrightarrow{} \mBbbN{}].
\mforall{}[a,b:E]. uiff((a <loc b);((fst(a)) = (fst(b))) \mwedge{} snd(a) < snd(b))
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_43_56
Last ObjectModification:
2015_01_27-PM-05_02_47
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