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Theorems · Theorem · order theory

le_ciInf_add

∀ {α : Type u_1} {ι : Sort u_2} [Nonempty ι] [inst : ConditionallyCompleteLattice α] [inst_1 : AddGroup α]
  [AddRightMono α] {a : α} {g : ι → α} {h : α}, (∀ (i : ι), a ≤ g i + h) → a ≤ iInf g + h
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Group
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
NonemptyConditionallyCompleteLatticeAddGroupAddRightMono
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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_ciInfciSup_add_le · cited by 1ciSup_add_leAddGroup · cited by 4410AddGroupiInf · cited by 1690iInfAddRightMono · cited by 367AddRightMonoConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…le_ciInf · cited by 32le_ciInfadd_neg_le_iff_le_add · cited by 6add_neg_le_iff_le_addle_ciInf_addCITED BYCITES

Cites6

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Cited by2

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