auto-task(exists_boost_mul_rotation): prove restricted Lorentz elements are a boost times a rotation#1350
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…ts are a boost times a rotation Co-authored-by: Claude <noreply@anthropic.com>
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Summary
Completes the TODO in
Physlib/Relativity/LorentzGroup/Restricted/Basic.lean:The homeomorphism
LorentzGroup.toBoostRotationinPhyslib/Relativity/LorentzGroup/Restricted/FromBoostRotation.leanalreadyprovides the boost–rotation decomposition; its file docstring states that the
inverse "writes elements of the restricted Lorentz group as a product of a
generalized boost and a rotation". This PR turns that into an explicit,
user-facing existence theorem and removes the now-satisfied TODO note.
Changes
LorentzGroup.exists_boost_mul_rotationtoFromBoostRotation.lean:for every
Λ : LorentzGroup.restricted dthere exist a velocityv : Lorentz.Velocity dand a rotationR : Rotations dwith(Λ : LorentzGroup d) = generalizedBoost 0 v * (R : LorentzGroup d).The proof uses the existing
toVelocity/toRotationmaps andmul_inv_cancel_left.TODO "..."marker fromRestricted/Basic.lean.How to review
exists_boost_mul_rotation; confirm its statementsays every restricted Lorentz element equals a generalized boost times a
rotation, and that it builds with no
sorry.TODO "Prove that every member of the restricted Lorentz group is combination of a boost and a rotation."note is gone fromRestricted/Basic.lean.lake build(project builds green; the theorem depends only onpropext,Classical.choice,Quot.sound— no new axioms).