Timelike order absolute
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.
FOR A CAUSAL SEPARATION EVERY OBSERVER BELOW c AGREES WHICH EVENT CAME FIRST. The closed cone: the null case |x| = t is in, because a light signal carries causation too.
Proposition
(p q t x : Int) (h : belowC p q) (hfuture : 0 < t) (hcausal : x*x ≤ t*t) : 0 < boostT p q t xProof
By obtain ⟨hq, hl, hr⟩ := 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--timelike_order_absolute
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
- Spacelike invariant
- Null invariant
- Spacelike order reverses
- Spacelike simultaneous
- Velocity addition below c