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,
length: ||as||,
map: map(f;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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
pi2: snd(t),
pi1: fst(t)
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:
2016_05_17-AM-08_45_59
Last ObjectModification:
2016_01_17-PM-02_38_02
Theory : event-ordering
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