Nuprl Lemma : frequency_wf
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. ∀[f:ℕ ⟶ T]. ∀[x:T]. ∀[p:ℕ]. ∀[q:ℕ+]. (frequency(f;x) ~ (p/q) ∈ ℙ)
Proof
Definitions occuring in Statement :
frequency: frequency(f;x) ~ (p/q),
nat_plus: ℕ+,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
frequency: frequency(f;x) ~ (p/q),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
nat_plus: ℕ+,
guard: {T},
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_wf,
exists_wf,
less_than_wf,
ratio-dist_wf,
seq-count_wf,
int_seg_subtype_nat,
false_wf,
less_than_transitivity2,
nat_plus_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
productEquality,
setElimination,
rename,
hypothesisEquality,
cumulativity,
applyEquality,
natural_numberEquality,
addEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
dependent_set_memberEquality,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. \mforall{}[x:T]. \mforall{}[p:\mBbbN{}]. \mforall{}[q:\mBbbN{}\msupplus{}]. (frequency(f;x) \msim{} (p/q) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-04_44_07
Last ObjectModification:
2015_12_27-PM-02_39_13
Theory : general
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