Theorems · Theorem · group theory
Submonoid.unit_mem_leftInv
∀ {M : Type u_1} [inst : Monoid M] (S : Submonoid M) (x : Mˣ), ↑x ∈ S → ↑x⁻¹ ∈ S.leftInv- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submonoidstatement and proof · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Submonoid.leftInvstatement · cited by 20
- Units.inv_valproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.leftInv_leftInv_eqproof · cited by 0