contractRight_mul_ι — Mathlib

English

Dually, contraction on the right with ι_Q a satisfies contractRight(b, d) = d(a) · b − (d ⌊ ι_Q a) · b for appropriate b ∈ Clifford(Q).

Русский

Справедливо для правого свёртывания: при контурах слева/справа выполняется равенство типа contractRight(b, d) = d(a) · b − (d ⌊ ι_Q a) · b.

LaTeX

$$$ contractRight(b, d) = d(a) \\cdot b - (d ⌊ ι_Q a) \\cdot b $$$

Lean4

/-- This is [grinberg_clifford_2016][] Theorem 12 -/
theorem contractRight_mul_ι (a : M) (b : CliffordAlgebra Q) : b * ι Q a⌊d = d a • b - b⌊d * ι Q a := by
  rw [contractRight_eq, reverse.map_mul, reverse_ι, contractLeft_ι_mul, map_sub, map_smul, reverse_reverse,
    reverse.map_mul, reverse_ι, contractRight_eq]

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