Spacelike invariant
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.
SPACELIKE STAYS SPACELIKE: no boost makes a spacelike separation reachable.
Proposition
(p q t x : Int) (h : belowC p q) (ht : interval t x < 0) : interval (boostT p q t x) (boostX p q t x) < 0Proof
By have hs := scale_positive p q h 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--spacelike_invariant
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
- The reverse boost undoes every boost
- Sq lt
- Lt of sq
- Interval scales
- Scale positive
- Timelike invariant
- Null invariant
- Timelike order absolute
- Spacelike order reverses
- Spacelike simultaneous
- Velocity addition below c