lTensor_inj_iff_rTensor_inj — Mathlib

English

Bijectivity equivalence between lTensor and rTensor holds as above.

Русский

Эквивалентность биективности между lTensor и rTensor выше.

LaTeX

$$$ \\mathrm{Bijective}(lTensor M f) \\iff \\mathrm{Bijective}(rTensor M f) $$$

Lean4

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

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