Theorems · Theorem · field theory
Commute.inv_sub_inv
∀ {K : Type u_1} [inst : DivisionRing K] {a b : K}, Commute a b → a ≠ 0 → b ≠ 0 → a⁻¹ - b⁻¹ = (b - a) / (a * b)- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
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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
- DivisionRingstatement and proof · cited by 1,062
- Commutestatement and proof · cited by 639
- inv_eq_one_divproof · cited by 33
- Commute.one_rightproof · cited by 22
- Commute.div_sub_divproof · cited by 2
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