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Theorems · Theorem

Equiv.nonempty_congr

∀ {α : Sort u} {β : Sort v} (e : α ≃ β), Nonempty α ↔ Nonempty β
Defined in
Mathlib.Logic.Equiv.Defs
Cited by
47 results in Mathlib
Foundations
Depth 14 from the axioms · uses Quot.sound
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Around this declaration

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

Matrix.isUnit_iff_isUnit_det · cited by 12Matrix.isUnit_iff_isUnit_…Algebra.FormallySmooth.iff_split_surjection · cited by 5FormallySmooth.iff_split_…Equiv.nonempty · cited by 4Equiv.nonemptyLinearOrderedCommGroup.wellFoundedOn_setOfPred_le_lt_iff_nonempty_discrete · cited by 3LinearOrderedCommGroup.we…CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_left · cited by 3IsUniversalColimit.nonemp…CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_pullbackCone_right · cited by 2IsUniversalColimit.nonemp…CategoryTheory.IsPushout.isVanKampen_iff · cited by 2IsPushout.isVanKampen_iffTrivSqZeroExt.isUnit_iff_isUnit_fst · cited by 2TrivSqZeroExt.isUnit_iff_…Matrix.isUnit_transpose · cited by 2Matrix.isUnit_transposeTopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover · cited by 2Presheaf.isSheaf_iff_isSh…SimpleGraph.compl_isIndContained_compl · cited by 2SimpleGraph.compl_isIndCo…CategoryTheory.Presheaf.isLimit_iff_isSheafFor · cited by 2Presheaf.isLimit_iff_isSh…TopCat.Presheaf.IsSheaf.isSheafOpensLeCover · cited by 2IsSheaf.isSheafOpensLeCov…CategoryTheory.PreGaloisCategory.initial_iff_fiber_empty · cited by 2PreGaloisCategory.initial…CategoryTheory.Functor.isConnected_iff_of_final · cited by 2Functor.isConnected_iff_o…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmNonempty.congr · cited by 6Nonempty.congrEquiv.nonempty_congrCITED BYCITES

Cites4

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

Cited by47

Results whose statement or proof uses this declaration.