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Theorems · Theorem · order theory

subset_upperBounds_mul

∀ {M : Type u_3} [inst : Mul M] [inst_1 : Preorder M] [MulLeftMono M] [MulRightMono M] (s t : Set M),
  upperBounds s * upperBounds t ⊆ upperBounds (s * t)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Bounds
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulPreorderMulLeftMonoMulRightMono
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Around this declaration

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

subset_lowerBounds_mul · cited by 1subset_lowerBounds_mulBddAbove.mul · cited by 1BddAbove.mulSet · cited by 53352SetPreorder · cited by 7952PreorderMulLeftMono · cited by 410MulLeftMonoSet.mul · cited by 297Set.mulMulRightMono · cited by 263MulRightMonoupperBounds · cited by 263upperBoundsSet.image2_subset_iff · cited by 30Set.image2_subset_iffmul_mem_upperBounds_mul · cited by 2mul_mem_upperBounds_mulsubset_upperBounds_mulCITED BYCITES

Cites8

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.