PRP0002canonicalv1Generator Distinctness
All five generators are pairwise distinct (immediate from K1 strict order).
Payload
Generator Distinctness
All five generators are pairwise distinct (immediate from K1 strict order).
Generator Distinctness
Summary
All five generators are pairwise distinct (immediate from K1 strict order).
Statement
\label{prop:gen-distinct}
All five generators are pairwise distinct:
\[
|\{\alpha, \pi, \gamma, \eta, \omega\}| = 5.
\]
Proof / Justification
A strict order is irreflexive: $\neg(x < x)$ for all $x$.
If any two generators were equal --- say $\alpha = \pi$ ---
then $\KAxiom{1}$ would give $\alpha < \alpha$,
contradicting irreflexivity.
Since $\KAxiom{1}$ places each pair of distinct generators
into a strict order relation,
no two can be equal.
Source Context
- Registry source:
book-01.jsonlline 12 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch01-five-generators.texlines 242-248
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Axioms - Name:
Tau.Kernel.gen_distinct
Dependencies
- Canonical: I.K1
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.P01generator-distinctnessprop:gen-distinctRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
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