### Nuprl Lemma : greatest-p-zero_wf

`∀[a:ℕ+ ⟶ ℤ]. ∀[n:ℕ].  (greatest-p-zero(n;a) ∈ ℕ)`

Proof

Definitions occuring in Statement :  greatest-p-zero: `greatest-p-zero(n;a)` nat_plus: `ℕ+` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` greatest-p-zero: `greatest-p-zero(n;a)` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` nat_plus: `ℕ+` int_seg: `{i..j-}` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` uimplies: `b supposing a` lelt: `i ≤ j < k` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` true: `True` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` guard: `{T}` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` bfalse: `ff`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation lambdaEquality applyEquality functionExtensionality addEquality setElimination rename productElimination dependent_functionElimination unionElimination voidElimination independent_functionElimination independent_isectElimination isect_memberEquality voidEquality intEquality because_Cache minusEquality equalityElimination equalityTransitivity equalitySymmetry approximateComputation dependent_pairFormation int_eqEquality axiomEquality functionEquality

Latex:
\mforall{}[a:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].  \mforall{}[n:\mBbbN{}].    (greatest-p-zero(n;a)  \mmember{}  \mBbbN{})

Date html generated: 2018_05_21-PM-03_22_04
Last ObjectModification: 2018_05_19-AM-08_19_00

Theory : rings_1

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