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Theorems · Theorem · logic and foundations

Filter.Germ.coe_lt

∀ {α : Type u} {β : Type v} {φ : Ultrafilter α} [inst : Preorder β] {f g : α → β}, ↑f < ↑g ↔ ∀ᶠ (x : α) in ↑φ, f x < g x
Defined in
Mathlib.Order.Filter.FilterProduct
Cited by
5 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

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

Hyperreal.ofSeq_lt_ofSeq · cited by 6Hyperreal.ofSeq_lt_ofSeqFilter.Germ.const_lt_iff · cited by 1Germ.const_lt_iffFilter.Germ.lt_def · cited by 0Germ.lt_defFilter.Germ.const_lt · cited by 0Germ.const_ltFilter.Germ.coe_pos · cited by 0Germ.coe_posPreorder · cited by 7952PreorderFilter.Eventually · cited by 3134Filter.EventuallyUltrafilter · cited by 193UltrafilterUltrafilter.toFilter · cited by 172Ultrafilter.toFilterFilter.Germ · cited by 102Filter.GermFilter.Germ.ofFun · cited by 73Germ.ofFunGerm.coe_ltCITED BYCITES

Cites6

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Cited by5

Results whose statement or proof uses this declaration.