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Theorems · Theorem · group theory

smul_right_surj_of_divisibleBy

Deprecated since 2026-04-19Use DivisibleBy.surjective_smul instead.

∀ (A : Type u_1) (α : Type u_2) [inst : AddMonoid A] [inst_1 : SMul α A] [inst_2 : Zero α] [DivisibleBy A α] {n : α},
  n ≠ 0 → Function.Surjective fun a => n • a

Alias of DivisibleBy.surjective_smul.

Defined in
Mathlib.GroupTheory.Divisible
Cited by
0 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddMonoidSMulZeroDivisibleBy
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AddMonoid · cited by 2864AddMonoidDivisibleBy · cited by 8DivisibleByDivisibleBy.surjective_smul · cited by 2DivisibleBy.surjective_sm…smul_right_surj_of_divisibleByCITED BYCITES

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