Lax Lean Archive

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Proof of `Compatibility and codimension of forward/reverse matrix restrictions` (1st statement)

groundedproofs/Lax342547Proofs/MixerCompatibility.lean · lax-342547

What this proof establishes

no assumptions

lem✓Lax342547.MixerCompatibility (1st statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

Choose left inverses UZ=1 and VW=1. For compatible A,B the explicit matrix UᵀA + BV - Uᵀ(ZᵀB)V has both prescribed restrictions. Necessity is associativity of matrix multiplication.