Below c composes to below c
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.
Proposition
∀ u ∈ subluminal, ∀ v ∈ subluminal, (add u v).num < (add u v).denProof
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--below_c_composes_to_below_c
Proved in the same file
- Light is the fixed point
- Light is fixed from either side
- Rest is the identity
- Composition is symmetric
- 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