Theorems · Theorem · commutative algebra
invOf_add_invOf
∀ {R : Type u_1} [inst : Semiring R] (a b : R) [inst_1 : Invertible a] [inst_2 : Invertible b],
⅟a + ⅟b = ⅟a * (a + b) * ⅟b- Defined in
- Mathlib.Algebra.Ring.Invertible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- SemiringInvertibleInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- add_commproof · cited by 1,535
- Invertiblestatement and proof · cited by 549
- mul_addproof · cited by 413
- add_mulproof · cited by 363
- Invertible.invOfstatement and proof · cited by 268
- mul_invOf_selfproof · cited by 28
- invOf_mul_selfproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- Ring.inverse_add_inverseproof · cited by 1
- inv_add_inv'proof · cited by 1