Theorems · Theorem · group theory
nsmul_eq_nsmul_of_modEq
∀ {G : Type u_1} [inst : AddMonoid G] {x : G} {n a b : ℕ}, a ≡ b [MOD n] → n • x = 0 → a • x = b • x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- add_zeroproof · cited by 2,707
- le_totalproof · cited by 294
- Nat.ModEqstatement and proof · cited by 225
- nsmul_zeroproof · cited by 73
- add_nsmulproof · cited by 44
- mul_nsmulproof · cited by 24
- le_iff_exists_addproof · cited by 16
- Nat.add_modEq_left_iffproof · cited by 4
- Nat.left_modEq_add_iffproof · cited by 1
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