Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The earlier flatness page is the commutative specialization; this page records the arbitrary-handed version used in balance
Definition
The earlier flatness result treats modules over a commutative ring, where the two handedness conventions coincide. The balance argument here instead needs both statements: a projective right module makes exact, and a projective left module makes exact. The preceding lemma records that arbitrary-ring version; this remark adds no second proof of it.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
12 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Weibel, An Introduction to Homological Algebra (standard reference, not scraped)