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Theorems · Theorem · logic and foundations

ZFSet.Definable.out_equiv

∀ {n : ℕ} (f : (Fin n → ZFSet.{u}) → ZFSet.{u}) [inst : ZFSet.Definable n f] {xs ys : Fin n → PSet.{u}},
  (∀ (i : Fin n), xs i ≈ ys i) → ZFSet.Definable.out f xs ≈ ZFSet.Definable.out f ys
Defined in
Mathlib.SetTheory.ZFC.Basic
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
ZFSet.Definable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ZFSet.Definable₁.out_equiv · cited by 1Definable₁.out_equivZFSet.Definable₂.out_equiv · cited by 0Definable₂.out_equivZFSet · cited by 259ZFSetPSet · cited by 107PSetZFSet.mk · cited by 17ZFSet.mkQuotient.eq_iff_equiv · cited by 6Quotient.eq_iff_equivZFSet.Definable.mk_out · cited by 3Definable.mk_outZFSet.mk_eq · cited by 2ZFSet.mk_eqZFSet.Definable.out · cited by 2Definable.outZFSet.Definable · cited by 2ZFSet.DefinableDefinable.out_equivCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.