### 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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