Theorems · Theorem · field theory
Commute.inv_add_inv
∀ {K : Type u_1} [inst : DivisionSemiring K] {a b : K}, Commute a b → a ≠ 0 → b ≠ 0 → a⁻¹ + b⁻¹ = (a + b) / (a * b)- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
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.
- Commutestatement and proof · cited by 639
- DivisionSemiringstatement and proof · cited by 216
- inv_eq_one_divproof · cited by 33
- Commute.one_div_add_one_divproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- inv_add_invproof · cited by 0