subset — Mathlib

English

If B1 ⊆ B2, then FreimanIso n A B1 f implies FreimanIso n A B2 f.

Русский

Если B1 ⊆ B2, то FreimanIso n A B1 f имплицирует FreimanIso n A B2 f.

LaTeX

$$subset (hB) (hf) (hf' ) : IsMulFreimanIso n A B1 f$$

Lean4

@[to_additive]
theorem subset (hA : A₁ ⊆ A₂) (hf : IsMulFreimanIso n A₂ B₂ f) (hf' : BijOn f A₁ B₁) : IsMulFreimanIso n A₁ B₁ f
    where
  bijOn := hf'
  map_prod_eq_map_prod s t hsA htA hs
    ht := by refine hf.map_prod_eq_map_prod (fun a ha ↦ hA (hsA ha)) (fun a ha ↦ hA (htA ha)) hs ht

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