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Theorems · Theorem · logic and foundations

Quotient.eq

∀ {α : Sort u_1} {r : Setoid α} {x y : α}, ⟦x⟧ = ⟦y⟧ ↔ r x y
Defined in
Mathlib.Data.Quot
Cited by
50 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
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Around this declaration

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

Quotient.eq'' · cited by 44Quotient.eq''Quotient.eq' · cited by 14Quotient.eq'Multiset.coe_eq_coe · cited by 11Multiset.coe_eq_coeArchimedeanClass.mk_eq_mk · cited by 8ArchimedeanClass.mk_eq_mkWeierstrassCurve.Jacobian.smul_eq · cited by 7Jacobian.smul_eqAlgebraicGeometry.Scheme.PartialMap.toRationalMap_eq_iff · cited by 7PartialMap.toRationalMap_…WeierstrassCurve.Projective.smul_eq · cited by 7Projective.smul_eqMulArchimedeanClass.mk_eq_mk · cited by 6MulArchimedeanClass.mk_eq…Quotient.eq_iff_equiv · cited by 6Quotient.eq_iff_equivMultiset.ext · cited by 6Multiset.extQuotient.mk_eq_iff_out · cited by 4Quotient.mk_eq_iff_outEquivalence.quot_mk_eq_iff · cited by 4Equivalence.quot_mk_eq_iffQuotient.eq_mk_iff_out · cited by 4Quotient.eq_mk_iff_outPath.Homotopic.Quotient.eq · cited by 3Quotient.eqZFSet.eq · cited by 3ZFSet.eqQuotient.eqCITED BYCITES

Cites0

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

Nothing in Mathlib beyond the foundations.

Cited by50

Results whose statement or proof uses this declaration.