Theorems · Definition · commutative algebra
RingEquiv.subringCongr
{R : Type u} → [inst : NonAssocRing R] → {s t : Subring R} → s = t → ↥s ≃+* ↥tMakes the identity isomorphism from a proof two subrings of a multiplicative monoid are equal.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- RingEquivstatement · cited by 1,147
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Equiv.setCongrproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Subfield.lift_relrank_map_mapproof · cited by 4
- LaurentSeries.powerSeriesRingEquivproof · cited by 1
- IsDiscreteValuationRing.equivValuationSubringproof · cited by 0
- RingEquiv.subringCongr_symmstatement · cited by 0
- RingEquiv.coe_subringCongr_applystatement · cited by 0