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Theorems · Theorem · order theory

le_add_ciInf

∀ {α : Type u_1} {ι : Sort u_2} [Nonempty ι] [inst : ConditionallyCompleteLattice α] [inst_1 : AddGroup α]
  [AddLeftMono α] {a g : α} {h : ι → α}, (∀ (j : ι), a ≤ g + h j) → a ≤ g + iInf h
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Group
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
NonemptyConditionallyCompleteLatticeAddGroupAddLeftMono
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Around this declaration

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

le_ciInf_add_ciInf · cited by 2le_ciInf_add_ciInfadd_ciSup_le · cited by 1add_ciSup_leAddGroup · cited by 4410AddGroupiInf · cited by 1690iInfAddLeftMono · cited by 687AddLeftMonoConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…le_ciInf · cited by 32le_ciInfneg_add_le_iff_le_add · cited by 6neg_add_le_iff_le_addle_add_ciInfCITED BYCITES

Cites6

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Cited by2

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