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Theorems · Theorem · order theory

le_mul_ciInf

∀ {α : Type u_1} {ι : Sort u_2} [Nonempty ι] [inst : ConditionallyCompleteLattice α] [inst_1 : Group α] [MulLeftMono 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
NonemptyConditionallyCompleteLatticeGroupMulLeftMono
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Around this declaration

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

mul_ciSup_le · cited by 1mul_ciSup_lele_ciInf_mul_ciInf · cited by 0le_ciInf_mul_ciInfGroup · cited by 6238GroupiInf · cited by 1690iInfMulLeftMono · cited by 410MulLeftMonoConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…le_ciInf · cited by 32le_ciInfinv_mul_le_iff_le_mul · cited by 5inv_mul_le_iff_le_mulle_mul_ciInfCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.