Theorems · Theorem · order theory

ciSup_mul_le

∀ {α : Type u_1} {ι : Sort u_2} [Nonempty ι] [inst : ConditionallyCompleteLattice α] [inst_1 : Group α] [MulRightMono α]
  {a : α} {g : ι → α} {h : α}, (∀ (i : ι), g i * h ≤ a) → iSup g * h ≤ a

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Group
Cited by: 1 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Quot.sound
Assumes: Nonempty ConditionallyCompleteLattice Group MulRightMono

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites5

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

Groupstatement and proof · cited by 6,238
iSupstatement · cited by 2,415
ConditionallyCompleteLatticestatement and proof · cited by 364
MulRightMonostatement and proof · cited by 263
le_ciInf_mulproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

ciSup_mul_ciSup_leproof · cited by 0