lTensor_bij_iff_rTensor_bij — Mathlib

English

If f,g are LinearEquivs, then congr (f.trans f') (g.trans g') equals (congr f g).trans (congr f' g').

Русский

Если f,g — линейные эквиваленты, то congr (f.trans f') (g.trans g') = (congr f g).trans (congr f' g').

LaTeX

$$$ congr (f.trans f') (g.trans g') = (congr f g).trans (congr f' g') $$$

Lean4

/-- Given a linear map `f : N → P`, `f ⊗ M` is bijective if and only if `M ⊗ f` is bijective. -/
theorem lTensor_bij_iff_rTensor_bij : Function.Bijective (lTensor M f) ↔ Function.Bijective (rTensor M f) := by
  simp [← comm_comp_rTensor_comp_comm_eq]

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