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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
ranked-eo: ranked-eo(L;rk),
es-locl: (e <loc e'),
pi1: fst(t),
pi2: snd(t),
mk-extended-eo: mk-extended-eo,
es-causl: (e < e'),
es-loc: loc(e),
all: ∀x:A. B[x],
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
infix_ap: x f y,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
int_seg: {i..j-},
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
Id: Id,
sq_type: SQType(T),
implies: P ⇒ Q,
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
es-E: E,
record-select: r.x,
record-update: r[x := v],
so_lambda: λ2x.t[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
so_apply: x[s],
nat: ℕ
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:
2016_05_17-AM-08_43_09
Last ObjectModification:
2016_01_17-PM-02_30_38
Theory : event-ordering
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