Mathlib Map

Theorems · Theorem

IsEmpty.false

∀ {α : Sort u} [self : IsEmpty α] (a : α), False
Defined in
Mathlib.Logic.IsEmpty.Defs
Cited by
24 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
IsEmpty
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Around this declaration

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

isEmptyElim · cited by 59isEmptyElimFunction.isEmpty · cited by 15Function.isEmptySet.univ_eq_empty_iff · cited by 13Set.univ_eq_empty_iffIsEmpty.elim' · cited by 12IsEmpty.elim'IsEmpty.exists_iff · cited by 7IsEmpty.exists_iffwellFounded_iff_isEmpty_descending_chain · cited by 5wellFounded_iff_isEmpty_d…SSet.Subcomplex.PairingCore.isRegular_pairing_iff · cited by 4PairingCore.isRegular_pai…Manifold.IsImmersionOfComplement.isImmersion · cited by 4IsImmersionOfComplement.i…cocompact_le_atBot · cited by 3cocompact_le_atBotisEmpty_iff · cited by 3isEmpty_iffCategoryTheory.PreGaloisCategory.not_initial_of_inhabited · cited by 3PreGaloisCategory.not_ini…Profinite.exists_locallyConstant · cited by 2Profinite.exists_locallyC…Function.Surjective.isEmpty · cited by 2Surjective.isEmptycoe_basisOfPiSpaceOfLinearIndependent · cited by 2coe_basisOfPiSpaceOfLinea…cocompact_le_atBot_atTop · cited by 2cocompact_le_atBot_atTopIsEmpty · cited by 759IsEmptyIsEmpty.falseCITED BYCITES

Cites1

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

  • IsEmptystatement and proof · cited by 759

Cited by28

Results whose statement or proof uses this declaration.