contractRight_mul_algebraMap — Mathlib

English

ContractRight with an algebra map yields zero on the scalar contraction: contractRight (algebraMap r) d = 0.

Русский

Свёртывание справа с алгебраMap даёт ноль на скалярное свёртывание: contractRight(algebraMap r) d = 0.

LaTeX

$$$ contractRight\\_algebraMap\\_mul(R, Q, d, r) : algebraMap R (CliffordAlgebra Q) r \\lceil d = 0 $$$

Lean4

theorem contractRight_mul_algebraMap (a : CliffordAlgebra Q) (r : R) :
    a * algebraMap _ _ r⌊d = a⌊d * algebraMap _ _ r := by
  rw [← Algebra.commutes, contractRight_algebraMap_mul, Algebra.commutes]

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