Theorems · Theorem · field theory
Commute.one_div_add_one_div
∀ {K : Type u_1} [inst : DivisionSemiring K] {a b : K}, Commute a b → a ≠ 0 → b ≠ 0 → 1 / a + 1 / b = (a + b) / (a * b)- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_commproof · cited by 1,535
- Commutestatement and proof · cited by 639
- DivisionSemiringstatement and proof · cited by 216
- Commute.one_rightproof · cited by 22
- Commute.div_add_divproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Commute.inv_add_invproof · cited by 1
- one_div_add_one_divproof · cited by 1