Theorems · Theorem · ring theory
TrivSqZeroExt.invOf_eq_inv
∀ {R : Type u} {M : Type v} [inst : DivisionSemiring R] [inst_1 : AddCommGroup M] [inst_2 : Module Rᵐᵒᵖ M]
[inst_3 : Module R M] [SMulCommClass R Rᵐᵒᵖ M] (x : TrivSqZeroExt R M) [inst_5 : Invertible x], ⅟x = x⁻¹- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SMulCommClassstatement and proof · cited by 1,927
- MulOppositestatement and proof · cited by 1,135
- Invertiblestatement and proof · cited by 549
- MulOpposite.opproof · cited by 520
- Invertible.invOfstatement · cited by 268
- DivisionSemiringstatement and proof · cited by 216
- TrivSqZeroExtstatement and proof · cited by 180
- TrivSqZeroExt.fstproof · cited by 96
- TrivSqZeroExt.sndproof · cited by 83
- invOf_eq_invproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- TrivSqZeroExt.mul_inv_cancelproof · cited by 1