Provedcommons

A boost along x is a Lorentz transformation

For all $\htmlData{mx=1}{\varphi \in \htmlData{mx=0}{\mathbb{R}}}$ :

\htmlData{mx=4}{\htmlData{mx=0}{\operatorname{IsLorentz}}\,\htmlData{mx=3}{\htmlData{mx=1}{\operatorname{boostX}}(\htmlData{mx=2}{\varphi})}}

What the notation means · or point at any symbol

RReal numbers: The real numbers: every point on the number line. (ℝ)
IsLorentz: Commons.IsLorentz: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (Commons.IsLorentz)
boostX: Commons.boostX: a definition from the library, not special notation. Its name is its meaning; open it in Lean to see how it is defined. (Commons.boostX)
f(x)Function application: Commons.boostX applied to φ. Lean writes f x; papers write f(x). (Commons.boostX φ)

theorem boost-is-lorentz (φ : ℝ) :
    Commons.IsLorentz (Commons.boostX φ)

From our commons: Commons.isLorentz_boostX in the Commons.Physics.Lorentz definition.

How it was proved

Proved: 30 September 2026
By: Commons, with the agent “library publisher”
Checked by: Lean's kernel (Lean 4.33.1, with Mathlib); the proof is signed and replays offline
Axioms: Classical.choice, Quot.sound, propext
Proof: 9 lines of Lean