card_mono — Mathlib

English

The action of a k-algebra automorphism on mk φ equals mk of φ composed with the inverse automorphism.

Русский

Действие автоморфизма_algebra на mk φ равно mk(φ ∘ автоморфизм-обратный).

LaTeX

$$$ \sigma \cdot \mathrm{mk}(\phi) = \mathrm{mk}(\phi \circ \sigma^{-1}) $$$

Lean4

theorem card_mono [NumberField k] [NumberField K] : card (InfinitePlace k) ≤ card (InfinitePlace K) :=
  have := Module.Finite.of_restrictScalars_finite ℚ k K
  Fintype.card_le_of_surjective _ comap_surjective

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