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Theorems · Theorem · order theory

WithBot.lt_unbot_iff

∀ {α : Type u_1} {a : α} [inst : LT α] {x : WithBot α} (hx : x ≠ ⊥), a < x.unbot hx ↔ ↑a < x
Defined in
Mathlib.Order.WithBot
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
LT
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithZero.lt_unzero_iff · cited by 0WithZero.lt_unzero_iffSubmodule.length_quotient_lt · cited by 0Submodule.length_quotient…Bot.bot · cited by 4720Bot.botWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someWithBot.unbot · cited by 23WithBot.unbotWithBot.lt_unbot_iffCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.