Theorems · Theorem · group theory
AddCommGroup.nsmul_modEq_nsmul
∀ {M : Type u_1} [inst : AddCommMonoid M] {a b p : M} [IsAddTorsionFree M] {n : ℕ},
n ≠ 0 → (n • a ≡ n • b [PMOD n • p] ↔ a ≡ b [PMOD p])- Defined in
- Mathlib.Algebra.Group.ModEq
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidproof · cited by 2,864
- IsAddTorsionFreestatement and proof · cited by 155
- AddCommGroup.ModEqstatement · cited by 107
- mul_nsmulproof · cited by 24
- nsmul_right_injproof · cited by 21
- mul_nsmul'proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- AddCommGroup.ModEq.nsmul_cancelproof · cited by 0