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Theorems · Theorem

not_nontrivial_iff_subsingleton

∀ {α : Type u_1}, ¬Nontrivial α ↔ Subsingleton α
Defined in
Mathlib.Logic.Nontrivial.Defs
Cited by
23 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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subsingleton_or_nontrivial · cited by 161subsingleton_or_nontrivialnot_subsingleton_iff_nontrivial · cited by 21not_subsingleton_iff_nont…RingHom.codomain_trivial · cited by 7RingHom.codomain_trivialFinset.one_lt_card_iff_nontrivial · cited by 6Finset.one_lt_card_iff_no…Submodule.nontrivial_iff_ne_bot · cited by 3Submodule.nontrivial_iff_…Cardinal.one_lt_iff_nontrivial · cited by 3Cardinal.one_lt_iff_nontr…LieModule.nontrivial_lowerCentralSeriesLast · cited by 2LieModule.nontrivial_lowe…Submodule.nontrivial_iff · cited by 2Submodule.nontrivial_iffWithBot.denselyOrdered_set_iff_subsingleton · cited by 2WithBot.denselyOrdered_se…IsSimpleAddGroup.prime_card · cited by 2IsSimpleAddGroup.prime_ca…Module.notMem_support_iff · cited by 2Module.notMem_support_iffsubsingleton_of_disjoint_isClopen · cited by 2subsingleton_of_disjoint_…LocallyFiniteOrder.denselyOrdered_iff_subsingleton · cited by 1LocallyFiniteOrder.densel…alternatingGroup.isMulCommutative_iff_card_le_three · cited by 1alternatingGroup.isMulCom…HahnSeries.orderTop_nsmul_le_orderTop_pow · cited by 1HahnSeries.orderTop_nsmul…Nontrivial · cited by 2416Nontrivialnot_nontrivial_iff_subsinglet…CITED BYCITES

Cites1

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Cited by23

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