lTensor_ker_subtype_tensorKerEquiv_symm

English

Symmetry of the lTensor with subtype ker f under the kernel equivalence, showing commutation with subtype embeddings.

Русский

Симметрия lTensor c подпорогом ker f в рамках эквивалентности ядра демонстрирует совместимость с вложениями подписи.

LaTeX

$$$(lTensor M (ker f).subtype) ((tensorKerEquiv S M f).symm x) = x$$$

Lean4

@[simp]
theorem lTensor_ker_subtype_tensorKerEquiv_symm [Module.Flat R M] (x : ker (AlgebraTensorModule.lTensor S M f)) :
    (lTensor M (ker f).subtype) ((tensorKerEquiv S M f).symm x) = x :=
  lTensor_ker_subtype_tensorKerInv S M f x

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