Mathlib Map

Theorems · Theorem

IsEmpty.exists_iff

∀ {α : Sort u} [IsEmpty α] {p : α → Prop}, (∃ a, p a) ↔ False
Defined in
Mathlib.Logic.IsEmpty.Defs
Cited by
7 results in Mathlib
Foundations
Depth 6 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.

MulAction.IsBlock.eq_univ_of_card_lt · cited by 3IsBlock.eq_univ_of_card_ltPSet.notMem_empty · cited by 2PSet.notMem_emptyAddAction.IsBlock.eq_univ_of_card_lt · cited by 1IsBlock.eq_univ_of_card_ltAddSubmonoid.mem_iSup_prop · cited by 0AddSubmonoid.mem_iSup_propSimpleGraph.not_isHamiltonian_of_isEmpty · cited by 0SimpleGraph.not_isHamilto…AddSubgroup.mem_iSup_prop · cited by 0AddSubgroup.mem_iSup_propAddSubsemigroup.mem_iSup_prop · cited by 0AddSubsemigroup.mem_iSup_…IsEmpty · cited by 759IsEmptyIsEmpty.false · cited by 24IsEmpty.falseIsEmpty.exists_iffCITED BYCITES

Cites2

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

Cited by7

Results whose statement or proof uses this declaration.