Theorems · Theorem · field theory
Commute.div_add_div
∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c d : K},
Commute b c → Commute b d → b ≠ 0 → d ≠ 0 → a / b + c / d = (a * d + b * c) / (b * d)- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 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.
Cites5
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
- Commute.eqproof · cited by 91
- add_divproof · cited by 89
- mul_div_mul_rightproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- div_add_divproof · cited by 4
- Commute.div_sub_divproof · cited by 2
- Commute.one_div_add_one_divproof · cited by 2
- Rat.cast_add_of_ne_zeroproof · cited by 2
- NNRat.cast_add_of_ne_zeroproof · cited by 1