contMDiffWithinAt_transContinuousLinearEquiv_left

English

The operation of product construction on two transported diffeomorphisms is itself a transported diffeomorphism on product spaces, with the natural projection maps forming the diffeomorphism.

Русский

Операция произведения двух преобразований остаётся преобразованием на произведениях пространств, с естественными проекциями forming диффеоморфизм.

LaTeX

$$$\text{prodCongr}(h_1,h_2) \colon M \times N \to M' \times N'$ is a transported diffeomorphism$$

Lean4

@[simp]
theorem contMDiffWithinAt_transContinuousLinearEquiv_left {f : M → M'} {x s} :
    ContMDiffWithinAt (I.transContinuousLinearEquiv e) I' n f s x ↔ ContMDiffWithinAt I I' n f s x :=
  ((toTransContinuousLinearEquiv I M e).contMDiffWithinAt_comp_diffeomorph_iff le_rfl).symm

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