Corpus v3 · Definition
cid001049
DEF0047canonicalv1Bounded Powerset
P_tau(X) = set of all divisors of X. Always finite: |P_tau(X)| = product of (e_i + 1) over prime factorization. No Russell paradox: strict divisibility decreases value.
Payload
Bounded Powerset
| P_tau(X) = set of all divisors of X. Always finite: | P_tau(X) | = product of (e_i + 1) over prime factorization. No Russell paradox: strict divisibility decreases value. |
Bounded Powerset
Summary
| P_tau(X) = set of all divisors of X. Always finite: | P_tau(X) | = product of (e_i + 1) over prime factorization. No Russell paradox: strict divisibility decreases value. |
Statement
%
\label{def:bounded-powerset}
For $\underline{x} \in \tau\text{-Idx}$,
the \textbf{$\tau$-powerset} of $\underline{x}$ is:
\[
\boxed{%
\mathcal{P}_\tau(\underline{x})
\;:=\;
\{\underline{a} \in \tau\text{-Idx}
: \underline{a} \in_\tau \underline{x}\}
\;=\;
\{\underline{a} : \underline{a} \mid \underline{x}\}.}
\]
That is, $\mathcal{P}_\tau(\underline{x})$
is the set of all \textbf{divisors} of $\underline{x}$.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 81 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part08/ch34-bounded-powerset.texlines 38-54
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Sets.Powerset - Name:
Tau.Sets.tau_divisors
Dependencies
- Canonical: I.D31, I.D32, I.T09
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.D33bounded-powersetdef:bounded-powersetRelease 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.