The reverse boost undoes every boost
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.
…and for EVERY event and EVERY boost, proved rather than decided: the theorem above checks eight events under five boosts; this holds for all integers p, q, t, x at once. Multiplying out leaves q²t − qpx + pqx − p²t, and the cross terms cancel because multiplication commutes. A proof, not an exhaustion — it rests on the standard axioms propext and Quot.sound that core's integer lemmas carry.
Proposition
∀ p q t x : Int, boostT (-p) q (boostT p q t x) (boostX p q t x) = (q * q - p * p) * t ∧ boostX (-p) q (boostT p q t x) (boostX p q t x) = (q * q - p * p) * xProof
By intro p q t x in spacetime.lean. Checked by the Lean kernel: it rests on Quot.sound and propext and on no other 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--the_reverse_boost_undoes_every_boost
Proved in the same file
- Light is the fixed point
- Light is fixed from either side
- Rest is the identity
- 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
- 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