Theorems · Theorem · group theory
Ne.isUnit
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a : G₀}, a ≠ 0 → IsUnit aAlias of the reverse direction of isUnit_iff_ne_zero.
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 182 definitions · 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.
- IsUnitstatement · cited by 1,602
- GroupWithZerostatement and proof · cited by 691
- isUnit_iff_ne_zeroproof · cited by 30
Cited by99
Results whose statement or proof uses this declaration.
- div_selfproof · cited by 237
- mul_div_cancel₀proof · cited by 77
- eq_div_iffproof · cited by 38
- div_eq_iffproof · cited by 37
- mul_div_mul_leftproof · cited by 25
- div_eq_div_iffproof · cited by 22
- eq_div_iff_mul_eqproof · cited by 19
- mul_div_mul_rightproof · cited by 16
- div_eq_one_iff_eqproof · cited by 16
- one_div_mul_cancelproof · cited by 14
- inv_mul_eq_iff_eq_mul₀proof · cited by 12
- div_left_inj'proof · cited by 11