Rest is the identity

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.

REST IS THE IDENTITY. Adding nothing changes nothing — the other distinguished element.

Proposition

∀ v ∈ sample, same (add rest v) v = 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--rest_is_the_identity

Proved in the same file

• Light is the fixed point
• Light is fixed from either side
• Composition is symmetric
• 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