Theorems · Theorem · field theory
Commute.div_sub_div
∀ {K : Type u_1} [inst : DivisionRing 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
- 2 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivisionRingstatement and proof · cited by 1,062
- Commutestatement and proof · cited by 639
- mul_negproof · cited by 590
- neg_divproof · cited by 161
- Commute.neg_rightproof · cited by 7
- Commute.div_add_divproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- div_sub_divproof · cited by 8
- Commute.inv_sub_invproof · cited by 0