Theorems · Definition · order theory
Partition.removeBot
{α : Type u_1} → {s : α} → [inst : CompleteLattice α] → (P : Set α) → sSupIndep P → sSup P = s → Partition sA constructor for Partition s that removes ⊥ from the set of parts.
- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Bot.botproof · cited by 4,720
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- Partitionstatement · cited by 91
- sSupIndepstatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- Partition.top_defstatement · cited by 1
- Partition.mem_removeBotstatement · cited by 1
- Partition.coe_removeBotstatement and proof · cited by 1
- Partition.removeBot.congr_simpstatement and proof · cited by 0