Theorems · Theorem · commutative algebra
Ring.inverse_add_inverse
∀ {R : Type u_1} [inst : Semiring R] {a b : R},
(IsUnit a ↔ IsUnit b) → Ring.inverse a + Ring.inverse b = Ring.inverse a * (a + b) * Ring.inverse bA version of inv_add_inv' for Ring.inverse.
- Defined in
- Mathlib.Algebra.Ring.Invertible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- IsUnitstatement and proof · cited by 1,602
- 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_add_invproof · cited by 0