Theorems · Theorem · group theory
eq_div_iff_mul_eq
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a b c : G₀}, c ≠ 0 → (a = b / c ↔ a * c = b)- Cited by
- 19 results in Mathlib
- Foundations
- Depth 25 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.
- GroupWithZerostatement and proof · cited by 691
- Ne.isUnitproof · cited by 99
- IsUnit.eq_div_iffproof · cited by 3
Cited by19
Results whose statement or proof uses this declaration.
- Nat.cast_chooseproof · cited by 6
- Real.sin_pi_over_two_pow_succproof · cited by 6
- Rat.cast_divInt_of_ne_zeroproof · cited by 5
- Rat.cast_injectiveproof · cited by 5
- Real.Angle.cos_eq_iff_coe_eq_or_eq_negproof · cited by 3
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- add_div_eq_mul_add_divproof · cited by 3
- Affine.Simplex.faceOppositeCentroid_mem_ninePointCircleproof · cited by 2
- FractionalIdeal.not_inv_le_one_of_ne_botproof · cited by 2
- div_smul_div_commproof · cited by 1
- Nat.cast_choose_eq_descPochhammer_divproof · cited by 1
- Nat.cast_choose_twoproof · cited by 1