Theorems · Theorem · group theory
div_self_mul_self
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] (a : G₀), a / a * a = aDividing a by itself and then multiplying by itself results in a, whether or not a is
zero.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- mul_inv_mul_cancelproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- gaugeRescale_smulproof · cited by 1