Theorems · Theorem · order theory
iSup_bot
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α], ⨆ x, ⊥ = ⊥- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- bot_uniqueproof · cited by 57
- iSup_const_leproof · cited by 5
Cited by29
Results whose statement or proof uses this declaration.
- Set.iUnion_emptyproof · cited by 68
- Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInfproof · cited by 5
- OrdinalApprox.lfpApprox_zeroproof · cited by 4
- DirectedOn.inf_sSup_eqproof · cited by 3
- iSup_ne_bot_subtypeproof · cited by 3
- Order.Ideal.biSup_mem_iffproof · cited by 3
- SSet.Subcomplex.Pairing.RankFunction.filtration_botproof · cited by 3
- nhdsWithin_biUnionproof · cited by 2
- tprod_iSup_decode₂proof · cited by 2
- AlgebraicGeometry.compact_open_induction_onproof · cited by 2
- Set.Finite.iInf_biSup_of_monotoneproof · cited by 2
- iSup_emptysetproof · cited by 2