Theorems · Theorem · commutative algebra
Ring.inverse_sub_inverse
∀ {R : Type u_1} [inst : Ring R] {a b : R},
(IsUnit a ↔ IsUnit b) → Ring.inverse a - Ring.inverse b = Ring.inverse a * (b - a) * Ring.inverse bA version of inv_sub_inv' for Ring.inverse.
- Defined in
- Mathlib.Algebra.Ring.Invertible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- IsUnitstatement and proof · cited by 1,602
- sub_selfproof · cited by 996
- Invertibleproof · cited by 549
- Iff.notproof · cited by 489
- Invertible.invOfproof · cited by 268
- Ring.inversestatement · cited by 160
- Ring.inverse_non_unitproof · cited by 26
- IsUnit.nonempty_invertibleproof · cited by 16
- Ring.inverse_invertibleproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.inv_sub_invproof · cited by 0