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Theorems · Theorem · group theory

IsUnit.unit.congr_simp

∀ {M : Type u_1} [inst : Monoid M] {a a_1 : M} (e_a : a = a_1) (h : IsUnit a), h.unit = ⋯.unit
Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
14 results in Mathlib
Foundations
Depth 11 from the axioms · uses Classical.choice
Assumes
Monoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsLocalizedModule.iso_mk_one · cited by 5IsLocalizedModule.iso_mk_…spectrum.unit_mem_mul_comm · cited by 3spectrum.unit_mem_mul_commStandardEtalePair.hom_ext · cited by 3StandardEtalePair.hom_extspectrum.units_smul_resolvent · cited by 1spectrum.units_smul_resol…Module.FinitePresentation.exists_basis_localizedModule_powers · cited by 1FinitePresentation.exists…Prod.quasispectrum_eq · cited by 1Prod.quasispectrum_eqAlgebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one · cited by 1SubmersivePresentation.ex…Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule · cited by 1FinitePresentation.exists…LocalizedModule.lift_comp · cited by 1LocalizedModule.lift_compPi.quasispectrum_eq · cited by 1Pi.quasispectrum_eqIsLocalizedModule.map_iso_commute · cited by 1IsLocalizedModule.map_iso…Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial · cited by 1IsSmoothAt.exists_isStand…Valuation.associated_of_isUniformizer · cited by 0Valuation.associated_of_i…LocalizedModule.lift_mk_one · cited by 0LocalizedModule.lift_mk_o…Monoid · cited by 3887MonoidUnits · cited by 2804UnitsIsUnit · cited by 1602IsUnitIsUnit.unit · cited by 252IsUnit.unitunit.congr_simpCITED BYCITES

Cites4

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
  • IsUnitstatement and proof · cited by 1,602
  • IsUnit.unitstatement and proof · cited by 252

Cited by14

Results whose statement or proof uses this declaration.