Nuprl Lemma : mu-bound
∀[b:ℕ]. ∀[f:ℕb ⟶ 𝔹]. mu(f) ∈ ℕb supposing ∃n:ℕb. (↑(f n))
Proof
Definitions occuring in Statement :
mu: mu(f),
int_seg: {i..j-},
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
mu: mu(f),
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mu-ge-bound,
exists_wf,
int_seg_wf,
assert_wf,
bool_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
hypothesis,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
applyEquality,
functionEquality
Latex:
\mforall{}[b:\mBbbN{}]. \mforall{}[f:\mBbbN{}b {}\mrightarrow{} \mBbbB{}]. mu(f) \mmember{} \mBbbN{}b supposing \mexists{}n:\mBbbN{}b. (\muparrow{}(f n))
Date html generated:
2016_05_14-AM-07_29_53
Last ObjectModification:
2015_12_26-PM-01_26_21
Theory : int_2
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