injectiveDimension_le — Mathlib

English

For a retract h: X ⟶ Y, injectiveDimension X ≤ injectiveDimension Y.

Русский

Для retract: injectiveDimension X ≤ injectiveDimension Y.

LaTeX

$$$\text{Retract}(X,Y) \Rightarrow \operatorname{injectiveDimension}(X) \le \operatorname{injectiveDimension}(Y)$$$

Lean4

theorem injectiveDimension_le {X Y : C} (h : Retract X Y) : injectiveDimension X ≤ injectiveDimension Y :=
  sInf_le_sInf_of_subset_insert_top
    (fun n hn ↦
      by
      simp only [Set.mem_setOf_eq, not_top_lt, IsEmpty.forall_iff, implies_true, Set.insert_eq_of_mem] at hn ⊢
      intro i hi
      have := hn i hi
      exact h.hasInjectiveDimensionLT i)

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