Theorems · Theorem · group theory
IsUnit.mul_val_inv
∀ {M : Type u_1} [inst : Monoid M] {a : M} (h : IsUnit a), a * ↑h.unit⁻¹ = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
- 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
- Unitsstatement · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- IsUnit.unitstatement and proof · cited by 252
- Units.mul_invproof · cited by 67
Cited by29
Results whose statement or proof uses this declaration.
- IsNilpotent.isUnit_add_left_of_commuteproof · cited by 4
- IsUnit.isUnit_iff_mulLeft_bijectiveproof · cited by 4
- IsLocalization.commutesproof · cited by 4
- spectrum.unit_mem_mul_commproof · cited by 3
- IsNilpotent.isUnit_quotient_mk_iffproof · cited by 3
- exists_bijective_map_powersproof · cited by 3
- Module.End.isUnit_apply_inv_apply_of_isUnitproof · cited by 3
- Submonoid.LocalizationMap.mk'_mulproof · cited by 2
- Polynomial.scaleRoots_dvd_iffproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.coeff_seq_memproof · cited by 2
- Associates.isAtom_iffproof · cited by 2
- PowerSeries.IsWeierstrassFactorization.isWeierstrassDivisionproof · cited by 1