Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax17.StrongPathExtraction

Strong path extraction

concepts/Lax17/StrongPathExtraction.lean · lax-17

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    Theorem

    An ordered path in the meta-tree of a strong tree-of-sets system yields a strong path-of-sets system on its internal clusters.

    Lean source view on GitHub

    1import Lax17.PathOfSets
    2import Lax17.TreeOfSets
    3
    4/-!
    5---
    6title: Strong path extraction
    7type: theorem
    8---
    9An ordered path in the meta-tree of a strong tree-of-sets system yields a
    10strong path-of-sets system on its internal clusters.
    11-/
    12
    13namespace Lax17.StrongPathExtraction
    14
    15universe u
    16
    17/-- An ordered meta-tree path yields a strong path-of-sets system on its
    18internal clusters. -/
    19axiom strongPathExtraction :
    20 ∀ {V : Type u} [DecidableEq V] {G : SimpleGraph V}
    21 {m w ℓ : ℕ} (T : Lax17.TreeOfSets.StrongSystem G m w),
    22 0 < ℓ →
    23 Lax17.TreeOfSets.HasMetaPath T (ℓ + 2) →
    24 Nonempty (Lax17.PathOfSets.StrongSystem G ℓ w)
    25
    26end Lax17.StrongPathExtraction
    27
    Show Proof

    Builds on

    Used by

    none

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…