Mathlib Map

Theorems · Theorem · order theory

WithBot.exists

∀ {α : Type u_1} {p : WithBot α → Prop}, (∃ x, p x) ↔ p ⊥ ∨ ∃ x, p ↑x
Defined in
Mathlib.Order.WithBot
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
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Around this declaration

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

WithBot.isPredLimit_iff · cited by 1WithBot.isPredLimit_iffOrder.IsPredLimit.withBotCoe · cited by 0IsPredLimit.withBotCoeOrder.IsSuccLimit.withBotCoe · cited by 0IsSuccLimit.withBotCoeBot.bot · cited by 4720Bot.botWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someWithBot.existsCITED BYCITES

Cites3

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.