Nuprl Lemma : first-choosable_wf
∀[M:Type ⟶ Type]. ∀[t:ℕ+]. ∀[r:ℕt ⟶ (ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P]))]. (first-choosable(r;t) ∈ ℕ)
Proof
Definitions occuring in Statement :
first-choosable: first-choosable(r;t),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
int_seg: {i..j-},
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
natural_number: $n,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
first-choosable: first-choosable(r;t),
let: let,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
run-system: run-system(r;t),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
pi2: snd(t),
System: System(P.M[P]),
ldag: LabeledDAG(T),
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
less_than: a < b,
squash: ↓T,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[r:\mBbbN{}t {}\mrightarrow{} (\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P]))].
(first-choosable(r;t) \mmember{} \mBbbN{})
Date html generated:
2016_05_17-AM-10_54_57
Last ObjectModification:
2016_01_18-AM-00_11_50
Theory : process-model
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