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Theorems · Theorem · order theory

WithTop.iInf_coe_eq_top

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrderBot α] {f : ι → α}, ⨅ x, ↑(f x) = ⊤ ↔ IsEmpty ι
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Indexed
Cited by
3 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLinearOrderBot
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Around this declaration

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

ENat.iInf_natCast_eq_top · cited by 3ENat.iInf_natCast_eq_topWithTop.iInf_coe_lt_top · cited by 2WithTop.iInf_coe_lt_topENNReal.iInf_coe_eq_top · cited by 0ENNReal.iInf_coe_eq_topTop.top · cited by 9680Top.topWithTop · cited by 3754WithTopiInf · cited by 1690iInfWithTop.some · cited by 1128WithTop.someIsEmpty · cited by 759IsEmptyConditionallyCompleteLinearOrderBot · cited by 84ConditionallyCompleteLine…WithTop.iInf_coe_eq_topCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.