derivation_ext — Mathlib

English

Two derivations are equal if they agree on X and on the subalgebra generated by X.

Русский

Две производные равны, если они совпадают на X и на подполя, порождаемого X.

LaTeX

$$$D_1 X = D_2 X \Rightarrow D_1 = D_2$$$

Lean4

@[ext]
theorem derivation_ext {D₁ D₂ : Derivation R R[X] A} (h : D₁ X = D₂ X) : D₁ = D₂ :=
  Derivation.ext fun f =>
    Derivation.eqOn_adjoin (Set.eqOn_singleton.2 h) <| by simp only [adjoin_X, Algebra.coe_top, Set.mem_univ]

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