πs' — Mathlib

English

If l and m are comparable in the lexicographic order and l is greater than m, and every i in m.val has ord_I(i) < o, then every i in m.val also has ord_I(i) < o.

Русский

Если l и m упорядочены лексикографически и m меньше l, и для каждого i∈m.val ord_I(i) < o, тогда и для каждого i∈m.val ord_I(i) < o.

LaTeX

$$$\\forall i \\in m.\\mathrm{ord}_I(i) < o.$$$

Lean4

/-- The `ℤ`-linear map induced by precomposition of the projection
`π C (ord I · < o₂) → π C (ord I · < o₁)` for `o₁ ≤ o₂`. -/
@[simps!]
noncomputable def πs' {o₁ o₂ : Ordinal} (h : o₁ ≤ o₂) :
    LocallyConstant (π C (ord I · < o₁)) ℤ →ₗ[ℤ] LocallyConstant (π C (ord I · < o₂)) ℤ :=
  LocallyConstant.comapₗ ℤ ⟨(ProjRestricts C (fun _ hh ↦ lt_of_lt_of_le hh h)), (continuous_projRestricts _ _)⟩

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