Theorems · Theorem · commutative algebra
invOf_sub_invOf
∀ {R : Type u_1} [inst : Ring R] (a b : R) [inst_1 : Invertible a] [inst_2 : Invertible b], ⅟a - ⅟b = ⅟a * (b - a) * ⅟bA version of inv_sub_inv' for invOf.
- Defined in
- Mathlib.Algebra.Ring.Invertible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- RingInvertibleInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement and proof · cited by 268
- mul_subproof · cited by 201
- sub_mulproof · cited by 170
- mul_invOf_selfproof · cited by 28
- invOf_mul_selfproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- inv_sub_inv'proof · cited by 4
- Ring.inverse_sub_inverseproof · cited by 1