Alphabeta Math
CorollaryStatement: Literature-sourcedProof: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05
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Maximal integral manifolds partition the manifold

Statement

If D is an integrable distribution on M, then its maximal connected integral manifolds form a partition of M.

Facts & Assumptions

Given: An integrable distribution D on M.

[A1]

Maximal leaves are the equivalence classes of the leaf relation.

Proof

technique · direct
1.1

Every point of M lies in its own equivalence class, so the union of the [given] maximal leaves is all of M.

given
1.2

Distinct equivalence classes are disjoint. Therefore distinct maximal [given] connected integral manifolds are disjoint.

given
2.1

Hence the maximal connected integral manifolds partition M. [given] ∎

given

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

17 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