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Theorems · Theorem · order theory

IsBot.not_isMax

∀ {α : Type u_1} [inst : PartialOrder α] {a : α} [Nontrivial α], IsBot a → ¬IsMax a
Defined in
Mathlib.Order.Max
Cited by
1 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderNontrivial
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Around this declaration

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

IsBot.not_isTop · cited by 0IsBot.not_isTopPartialOrder · cited by 6410PartialOrderNontrivial · cited by 2416NontrivialLT.lt.le · cited by 2189lt.leIsMax · cited by 372IsMaxexists_ne · cited by 101exists_neIsBot · cited by 77IsBotIsMax.eq_of_ge · cited by 7IsMax.eq_of_geIsBot.lt_of_ne · cited by 1IsBot.lt_of_neIsBot.not_isMaxCITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.