galRestrict'_id — Mathlib

English

The restrict'-lift composition respects composition of maps: galRestrict' of a composition equals the composition of galRestrict' maps.

Русский

Сохранение композиции: galRestrict' от композиции равен композиции galRestrict'.

LaTeX

$$galRestrict'_comp (σ) (σ') : galRestrict' A B B₃ (σ'∘σ) = (galRestrict' A B₂ B₃ σ') ∘ (galRestrict' A B B₂ σ)$$

Lean4

@[simp]
theorem galRestrict'_id : galRestrict' A B B (.id K L) = .id A B :=
  by
  ext
  apply IsIntegralClosure.algebraMap_injective B A L
  simp

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