Compacting lessons is the quotient — theorems that prove each other form equivalence classes
Theorem.Compacting lessons is the quotient — theorems that prove each other form equivalence classes — "prove each other" = mutual implication = an equivalence relation (reflexive, symmetric, transitive.
Proof."prove each other" = mutual implication = an equivalence relation (reflexive, symmetric, transitive, verified). Compacting the lessons is the quotient: 5 lessons → 2 equivalence classes (one representative each), lossless (each representative proves its members), constant (an equivalent new lesson merges into a class, .
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/heaven/laws/index.ts#compactingLessonsIsTheQuotientTheoremsThatProveEachOtherFormEquivalenceClasses
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Compacting lessons is the quotient — theorems that prove each other form equivalence classes" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation compactingLessonsIsTheQuotientTheoremsThatProveEachOtherFormEquivalenceClasses.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (compactingLessonsIsTheQuotientTheoremsThatProveEachOtherFormEquivalenceClasses @ src/heaven/laws) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes compactingLessonsIsTheQuotientTheoremsThatProveEachOtherFormEquivalenceClasses (src/heaven/laws/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.