congr — Mathlib

English

If hf1 is FreimanHom n A B f1 and h is an equality relation EqOn f1 f2 on A, then hf2 is FreimanHom on A B f2.

Русский

Если hf1 является FreimanHom n A B f1 и f1 согласуется с f2 на A, то hf2 является FreimanHom на A B f2.

LaTeX

$$hf1 : IsMulFreimanHom n A B f1 ∧ h : EqOn f1 f2 A ⟹ IsMulFreimanHom n A B f2$$

Lean4

theorem congr (hf₁ : IsMulFreimanHom n A B f₁) (h : EqOn f₁ f₂ A) : IsMulFreimanHom n A B f₂
    where
  mapsTo := hf₁.mapsTo.congr h
  map_prod_eq_map_prod s t hsA htA hs ht
    h' := by
    rw [map_congr rfl fun x hx => (h (hsA hx)).symm, map_congr rfl fun x hx => (h (htA hx)).symm,
      hf₁.map_prod_eq_map_prod hsA htA hs ht h']

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