Nuprl Lemma : ranked-eo_wf
∀[Info:Type]. ∀[L:Id ⟶ (Info List)]. ∀[rk:(i:Id × ℕ||L i||) ⟶ ℕ].
ranked-eo(L;rk) ∈ EO+(Info) 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),
event-ordering+: EO+(Info),
Id: Id,
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],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ranked-eo: ranked-eo(L;rk),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
int_seg: {i..j-},
pi2: snd(t),
false: False,
implies: P ⇒ Q,
not: ¬A,
pi1: fst(t),
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
prop: ℙ,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
le: A ≤ B,
infix_ap: x f y,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T ,
rev_uimplies: rev_uimplies(P;Q),
less_than: a < b,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
Id: Id
Latex:
\mforall{}[Info:Type]. \mforall{}[L:Id {}\mrightarrow{} (Info List)]. \mforall{}[rk:(i:Id \mtimes{} \mBbbN{}||L i||) {}\mrightarrow{} \mBbbN{}].
ranked-eo(L;rk) \mmember{} EO+(Info) 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_40_01
Last ObjectModification:
2016_01_17-PM-02_38_30
Theory : event-ordering
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