Mathlib Map

Theorems · Theorem · group theory

OneMemClass.coe_eq_one

∀ {A : Type u_3} {M₁ : Type u_4} [inst : SetLike A M₁] [inst_1 : One M₁] [hA : OneMemClass A M₁] {S' : A} {x : ↥S'},
  ↑x = 1 ↔ x = 1
Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
6 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
SetLikeOneOneMemClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

HasEnoughRootsOfUnity.natCard_rootsOfUnity · cited by 5HasEnoughRootsOfUnity.nat…Submonoid.pow_exponent_eq_one · cited by 1Submonoid.pow_exponent_eq…Subalgebra.coe_eq_one · cited by 1Subalgebra.coe_eq_oneBoundedContinuousFunction.ext_of_char_eq · cited by 1BoundedContinuousFunction…Polynomial.int_monic_iff · cited by 0Polynomial.int_monic_iffNumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer · cited by 0fundamentalCone.integerSe…SetLike · cited by 1084SetLikeOneMemClass · cited by 21OneMemClassOneMemClass.coe_eq_oneCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.