Corpus v3 · Definition
cid001030
DEF0028canonicalv1Internal Divisibility
a | b iff exists k in tau-Idx such that b = a * k. Decidable, reflexive, transitive. First relational concept earned from Part III arithmetic.
Payload
Internal Divisibility
| a | b iff exists k in tau-Idx such that b = a * k. Decidable, reflexive, transitive. First relational concept earned from Part III arithmetic. |
Internal Divisibility
Summary
| a | b iff exists k in tau-Idx such that b = a * k. Decidable, reflexive, transitive. First relational concept earned from Part III arithmetic. |
Statement
%
\label{def:divisibility}
For $\underline{a}, \underline{b} \in \tau\text{-Idx}$,
we say $\underline{a}$ \textbf{divides} $\underline{b}$,
written $\underline{a} \mid \underline{b}$, if there exists
$\underline{k} \in \tau\text{-Idx}$ such that
$\underline{b} = \underline{a} \times \underline{k}$.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 51 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part04/ch16-primes-divisibility.texlines 43-51
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Coordinates.Primes - Name:
Tau.Coordinates.idx_divides
Dependencies
- Canonical: I.D10, I.D11
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
I.D19ainternal-divisibilitydef:divisibilityRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.