Mathlib Map

Theorems · Definition · order theory

Setoid.quotientQuotientEquivQuotient

{α : Type u_1} → (r s : Setoid α) → (h : r ≤ s) → Quotient (Setoid.ker (Quot.mapRight h)) ≃ Quotient s

The third isomorphism theorem for sets.

Defined in
Mathlib.Data.Setoid.Basic
Cited by
0 results in Mathlib
Foundations
Depth 10 from the axioms · uses Quot.sound
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Around this declaration

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RingCon.quotientQuotientEquivQuotient · cited by 3RingCon.quotientQuotientE…AddCon.quotientQuotientEquivQuotient · cited by 0AddCon.quotientQuotientEq…Con.quotientQuotientEquivQuotient · cited by 0Con.quotientQuotientEquiv…Equiv · cited by 8337EquivQuotient.mk'' · cited by 132Quotient.mk''Setoid.ker · cited by 43Setoid.kerQuotient.liftOn' · cited by 19Quotient.liftOn'Quot.mapRight · cited by 0Quot.mapRightSetoid.quotientQuotientEquivQ…CITED BYCITES

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