PracticalNumbers.lean`

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 0 contain sorry, 0 declared as axioms

Practical numbers

A positive integer $n$ is called a practical number if every positive integer $m ≤ n$ can be represented as a sum of distinct divisors of $n$.

References:

Main definitions

Nat.IsPractical: A natural number $n$ is practical if every positive integer $m ≤ n$ can be expressed as a sum of distinct divisors of $n$.

Imports (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

def Nat.IsPractical A natural number $n$ is practical if every positive integer $m ≤ n$ can be represented as a sum of distinct divisors of $n$ line 43 source
Source documentation
A natural number $n$ is practical if every positive integer $m ≤ n$ can be represented as a sum of distinct divisors of $n$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: LE.le, Membership.mem, Set, subsetSums, Finset, Nat.divisors
5 instances, coercions and auxiliary constants left out.
```
def IsPractical (n : ℕ) : Prop :=
…
```