EvenPart is symmetric

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and resting on no axiom beyond propext and Quot.sound. 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 unfold evenPart in involution.lean. Checked by the Lean kernel: it rests on propext and on no other axiom.

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