isTrivialRelation_iff_vanishesTrivially

English

A simplification lemma: equivalence comp preserves IsTrivialRelation after rewriting with vanishing trivially.

Русский

Лемма упрощения: эквивалентность сохраняет IsTrivialRelation после преобразований, приводящих к тривиальности.

LaTeX

$$Equiv.isTrivialRelation_comp {κ} [Fintype κ] (e : κ ≃ ι) : IsTrivialRelation (f ∘ e) (x ∘ e) ↔ IsTrivialRelation f x$$

Lean4

/-- `Module.IsTrivialRelation` is equivalent to the predicate `TensorProduct.VanishesTrivially`
defined in `Mathlib/LinearAlgebra/TensorProduct/Vanishing.lean`. -/
theorem isTrivialRelation_iff_vanishesTrivially : IsTrivialRelation f x ↔ VanishesTrivially R f x := by
  simp only [IsTrivialRelation, VanishesTrivially, smul_eq_mul, mul_comm]

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