Composition is symmetric

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked 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.

COMPOSITION IS SYMMETRIC in the two velocities, at every pair of the sample.

Proposition

∀ u ∈ sample, ∀ v ∈ sample, same (add u v) (add v u) = true

Proof

By decide in spacetime.lean. Checked by the Lean kernel: it depends on no axiom.

Sources and identifiers

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

Proved in the same file

• Light is the fixed point
• Light is fixed from either side
• Rest is the identity
• Below c composes to below c
• The boost preserves the interval
• The light cone is carried to itself
• The reverse boost undoes the boost
• The reverse boost undoes every boost
• Sq lt
• Lt of sq
• Interval scales
• Scale positive
• Timelike invariant
• Spacelike invariant
• Null invariant
• Timelike order absolute
• Spacelike order reverses
• Spacelike simultaneous
• Velocity addition below c

All machine-checked theorems