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Theorems · Theorem · order theory

inf_lt_iff

∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, min b c < a ↔ b < a ∨ c < a
Defined in
Mathlib.Order.Lattice
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

min_lt_iff · cited by 3min_lt_iffFinset.inf_lt_iff · cited by 1Finset.inf_lt_iffmin_lt_of_add_lt_two_nsmul · cited by 0min_lt_of_add_lt_two_nsmulCauSeq.inf_limZero · cited by 0CauSeq.inf_limZeroLinearOrder · cited by 8572LinearOrderinf_lt_iffCITED BYCITES

Cites1

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

Cited by4

Results whose statement or proof uses this declaration.