localInverse_isLocalDiffeomorphAt

English

Isomorphism between Pi-product models and their Component projections for a finite family.

Русский

Изоморфизм между продукцией Pi-моделей и их проекциями для конечной семьи.

LaTeX

$$$$ \text{ModelWithCorners pi is compatible with projections: } \text{(pi I)} = \prod_i I_i. $$$$

Lean4

theorem localInverse_isLocalDiffeomorphAt (hf : IsLocalDiffeomorphAt I J n f x) :
    IsLocalDiffeomorphAt J I n (hf.localInverse) (f x) :=
  hf.localInverse.isLocalDiffeomorphAt _ _ _ hf.localInverse_mem_source

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