Mathlib Map

Theorems · Definition · ring theory

RingEquiv.trans

{R : Type u_4} →
  {S : Type u_5} →
    {S' : Type u_6} →
      [inst : Mul R] →
        [inst_1 : Mul S] →
          [inst_2 : Add R] → [inst_3 : Add S] → [inst_4 : Mul S'] → [inst_5 : Add S'] → R ≃+* S → S ≃+* S' → R ≃+* S'

Transitivity of RingEquiv.

Defined in
Mathlib.Algebra.Ring.Equiv
Cited by
54 results in Mathlib
Foundations
Depth 20 from the axioms · uses Quot.sound
Assumes
MulMulAddAddMulAdd

Around this declaration

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

AlgEquiv.trans · cited by 108AlgEquiv.transPolynomial.opRingEquiv · cited by 13Polynomial.opRingEquivDoubleQuot.quotQuotEquivQuotOfLE · cited by 11DoubleQuot.quotQuotEquivQ…RingEquiv.quotientBot · cited by 8RingEquiv.quotientBotMvPolynomial.sumRingEquiv · cited by 8MvPolynomial.sumRingEquivIdeal.quotientMulEquivQuotientProd · cited by 8Ideal.quotientMulEquivQuo…Int.quotientSpanNatEquivZMod · cited by 7Int.quotientSpanNatEquivZ…IsLocalization.AtPrime.equivQuotMaximalIdeal · cited by 7AtPrime.equivQuotMaximalI…DoubleQuot.quotQuotEquivComm · cited by 7DoubleQuot.quotQuotEquivC…AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin · cited by 7AlgebraicIndependent.mvPo…Rat.IsIntegralClosure.intEquiv · cited by 6IsIntegralClosure.intEquivAdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot · cited by 6AdjoinRoot.quotAdjoinRoot…KummerDedekind.quotMapEquivQuotQuotMap · cited by 5KummerDedekind.quotMapEqu…Rat.HeightOneSpectrum.adicCompletion.padicEquiv · cited by 5adicCompletion.padicEquivOrderRingIso.trans · cited by 5OrderRingIso.transRingEquiv · cited by 1147RingEquivMulEquiv · cited by 1142MulEquivAddEquiv · cited by 1087AddEquivMulEquiv.toEquiv · cited by 126MulEquiv.toEquivMulEquiv.trans · cited by 53MulEquiv.transAddEquiv.trans · cited by 53AddEquiv.transRingEquiv.toMulEquiv · cited by 26RingEquiv.toMulEquivRingEquiv.toAddEquiv · cited by 13RingEquiv.toAddEquivAddEquiv.map_add' · cited by 5AddEquiv.map_add'MulEquiv.map_mul' · cited by 1MulEquiv.map_mul'RingEquiv.transCITED BYCITES

Cites10

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

Cited by107

Results whose statement or proof uses this declaration.