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Theorems · Theorem · order theory

Finpartition.parts_nonempty_iff

∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a : α} {P : Finpartition a}, P.parts.Nonempty ↔ a ≠ ⊥
Defined in
Mathlib.Order.Partition.Finpartition
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LatticeOrderBot
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Around this declaration

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

Finpartition.parts_nonempty · cited by 3Finpartition.parts_nonemp…Bot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotFinset.Nonempty · cited by 1001Finset.NonemptyLattice · cited by 916LatticeFinpartition · cited by 199FinpartitionFinpartition.parts · cited by 184Finpartition.partsFinpartition.parts_eq_empty_iff · cited by 2Finpartition.parts_eq_emp…Finpartition.parts_nonempty_i…CITED BYCITES

Cites7

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Cited by1

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