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Theorems · Theorem · logic and foundations

Set.one_lt_ncard

∀ {α : Type u_1} {s : Set α}, autoParam s.Finite Set.one_lt_ncard._auto_1 → (1 < s.ncard ↔ ∃ a ∈ s, ∃ b ∈ s, a ≠ b)
Defined in
Mathlib.Data.Set.Card
Cited by
4 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

MulAction.IsPreprimitive.of_prime_card · cited by 3IsPreprimitive.of_prime_c…MulAction.IsPreprimitive.is_two_motive_of_is_motive · cited by 2IsPreprimitive.is_two_mot…Set.one_lt_ncard_iff · cited by 1Set.one_lt_ncard_iffAddAction.IsPreprimitive.of_prime_card · cited by 0IsPreprimitive.of_prime_c…Set · cited by 53352SetSet.Finite · cited by 1814Set.FiniteSet.ncard · cited by 344Set.ncardSet.ncard_eq_toFinset_card · cited by 21Set.ncard_eq_toFinset_cardSet.one_lt_ncardCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.