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Theorems · Theorem · order theory

IsAtom.bot_covBy

∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, IsAtom a → ⊥ ⋖ a

Alias of the reverse direction of bot_covBy_iff.

Defined in
Mathlib.Order.Atoms
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ComplementedLattice.isStronglyAtomic · cited by 2ComplementedLattice.isStr…Lattice.isStronglyAtomic · cited by 1Lattice.isStronglyAtomicbot_covBy_top · cited by 0bot_covBy_topPartialOrder · cited by 6410PartialOrderBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotCovBy · cited by 290CovByIsAtom · cited by 130IsAtombot_covBy_iff · cited by 4bot_covBy_iffIsAtom.bot_covByCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.