EvenPart is symmetric

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, decided by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.

THE EVEN PART IS WHAT SURVIVES THE REFLECTION — it takes the same value at x and at σx.

Proposition

{α : Type} (f : α → Int) (σ : α → α) (h : IsInvolution σ) (x : α) : evenPart f σ (σ x) = evenPart f σ x

Proof

By by in involution.lean. The kernel reduces the proposition and reports no axiom dependency.

Sources and identifiers

• Lean source · src/pair/formal/proofs/involution.lean
• Typeset paper · src/research/lean-theorems.tex
• Repository deposit · doi:10.5281/zenodo.21787144
• Author · ORCID 0009-0000-7312-9778
• Deposit record · involution--evenPart_is_symmetric

Proved in the same file

• Orbit sums to zero
• Odd vanishes at a fixed point
• The split loses nothing
• The instance is an involution
• The instance cancels over every orbit
• The instance has one harmonic point
• The instance splits without loss

All machine-checked theorems