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Theorems · Theorem · order theory

Set.IsPWO.mul

∀ {α : Type u_1} {s t : Set α} [inst : CommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelMonoid α],
  s.IsPWO → t.IsPWO → (s * t).IsPWO
Defined in
Mathlib.Data.Finset.MulAntidiagonal
Cited by
2 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidPartialOrderIsOrderedCancelMonoid
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Around this declaration

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

Set.IsWF.mul · cited by 1IsWF.mulFinset.isPWO_support_mulAntidiagonal · cited by 0Finset.isPWO_support_mulA…Set · cited by 53352SetPartialOrder · cited by 6410PartialOrderCommMonoid · cited by 2264CommMonoidSet.mul · cited by 297Set.mulSet.IsPWO · cited by 99Set.IsPWOIsOrderedCancelMonoid · cited by 65IsOrderedCancelMonoidmonotone_fst · cited by 9monotone_fstmonotone_snd · cited by 9monotone_sndSet.IsPWO.image_of_monotone · cited by 5IsPWO.image_of_monotoneSet.image_mul_prod · cited by 4Set.image_mul_prodSet.IsPWO.prod · cited by 4IsPWO.prodMonotone.mul' · cited by 2Monotone.mul'IsPWO.mulCITED BYCITES

Cites12

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.