Nuprl Lemma : first-choosable-property
∀[M:Type ⟶ Type]. ∀[r:pRunType(P.M[P])]. ∀[t:ℕ+]. ∀[n:ℕ].
first-choosable(r;t) ≤ n supposing ↑lg-is-source(run-intransit(r;t);n)
Proof
Definitions occuring in Statement :
first-choosable: first-choosable(r;t),
run-intransit: run-intransit(r;t),
pRunType: pRunType(T.M[T]),
lg-is-source: lg-is-source(g;i),
nat_plus: ℕ+,
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
first-choosable: first-choosable(r;t),
let: let,
run-intransit: run-intransit(r;t),
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
ldag: LabeledDAG(T),
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
nat_plus: ℕ+,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:pRunType(P.M[P])]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbN{}].
first-choosable(r;t) \mleq{} n supposing \muparrow{}lg-is-source(run-intransit(r;t);n)
Date html generated:
2016_05_17-AM-10_55_04
Last ObjectModification:
2016_01_18-AM-00_13_43
Theory : process-model
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