Theorems · Theorem · group theory
invOf_smul_eq_iff
∀ {α : Type u_5} {β : Type u_6} [inst : Monoid α] [inst_1 : MulAction α β] {c : α} {x y : β} [inst_2 : Invertible c],
⅟c • x = y ↔ x = c • y- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- MonoidMulActionInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- MulActionstatement and proof · cited by 1,294
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement · cited by 268
- inv_smul_eq_iffproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- QuadraticMap.associated_eq_self_applyproof · cited by 7
- QuadraticMap.associated_left_inverseproof · cited by 1
- QuadraticMap.associated_left_inverse'proof · cited by 0