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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingEquivstatement and proof · cited by 1,147
- MulEquivproof · cited by 1,142
- AddEquivproof · cited by 1,087
- MulEquiv.toEquivproof · cited by 126
- MulEquiv.transproof · cited by 53
- AddEquiv.transproof · cited by 53
- RingEquiv.toMulEquivproof · cited by 26
- RingEquiv.toAddEquivproof · cited by 13
- AddEquiv.map_add'proof · cited by 5
- MulEquiv.map_mul'proof · cited by 1
Cited by107
Results whose statement or proof uses this declaration.
- AlgEquiv.transproof · cited by 108
- Polynomial.opRingEquivproof · cited by 13
- DoubleQuot.quotQuotEquivQuotOfLEproof · cited by 11
- RingEquiv.quotientBotproof · cited by 8
- MvPolynomial.sumRingEquivproof · cited by 8
- Ideal.quotientMulEquivQuotientProdproof · cited by 8
- Int.quotientSpanNatEquivZModproof · cited by 7
- IsLocalization.AtPrime.equivQuotMaximalIdealproof · cited by 7
- DoubleQuot.quotQuotEquivCommproof · cited by 7
- AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoinproof · cited by 7
- Rat.IsIntegralClosure.intEquivproof · cited by 6
- AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuotproof · cited by 6