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Theorems · Theorem · order theory

WithBot.bot_ne_coe

∀ {α : Type u_1} {a : α}, ⊥ ≠ ↑a
Defined in
Mathlib.Order.WithBot
Cited by
12 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
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Around this declaration

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

Interval.bot_ne_pure · cited by 3Interval.bot_ne_pureWithBot.isPredPrelimit_iff · cited by 2WithBot.isPredPrelimit_iffWithBot.bot_ne_zero · cited by 2WithBot.bot_ne_zeroWithBot.isPredLimit_iff · cited by 1WithBot.isPredLimit_iffWithBot.isPredPrelimit_bot · cited by 1WithBot.isPredPrelimit_botWithBot.isSuccPrelimit_iff · cited by 1WithBot.isSuccPrelimit_iffWithBot.bot_ne_natCast · cited by 1WithBot.bot_ne_natCastWithBot.covBy_bot_iff · cited by 1WithBot.covBy_bot_iffBoxIntegral.Box.splitLower_ne_splitUpper · cited by 1Box.splitLower_ne_splitUp…Finset.max_erase_ne_self · cited by 1Finset.max_erase_ne_selfWithBot.isPredLimit_bot · cited by 0WithBot.isPredLimit_botWithBot.bot_ne_one · cited by 0WithBot.bot_ne_oneBot.bot · cited by 4720Bot.botWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someWithBot.bot_ne_coeCITED BYCITES

Cites3

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

Cited by12

Results whose statement or proof uses this declaration.