Theorems · Theorem · group theory
IsUnit.div_mul_cancel
∀ {α : Type u} [inst : DivisionMonoid α] {b : α}, IsUnit b → ∀ (a : α), a / b * b = a- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- div_eq_mul_invproof · cited by 715
- DivisionMonoidstatement and proof · cited by 201
- IsUnit.inv_mul_cancel_rightproof · cited by 2
Cited by37
Results whose statement or proof uses this declaration.
- div_mul_cancel₀proof · cited by 122
- Collinear.mem_affineSpan_of_mem_of_neproof · cited by 7
- Complex.norm_mul_exp_arg_mul_Iproof · cited by 6
- Real.sin_pi_over_two_pow_succproof · cited by 6
- IsUnit.mul_div_cancelproof · cited by 5
- div_mul_cancel_of_impproof · cited by 5
- hasSum_geometric_two'proof · cited by 4
- tendsto_exp_mul_div_rpow_atTopproof · cited by 3
- WeierstrassCurve.Projective.equiv_of_Z_eq_zeroproof · cited by 3
- wbtw_smul_vadd_smul_vadd_of_nonneg_of_leproof · cited by 3
- InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zeroproof · cited by 3
- IsUnit.div_eq_div_iffproof · cited by 3