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Theorems · Theorem · order theory

Monotone.vadd

∀ {G : Type u_1} {P : Type u_2} {γ : Type u_3} [inst : Preorder G] [inst_1 : Preorder P] [inst_2 : Preorder γ]
  [inst_3 : VAdd G P] [IsOrderedVAdd G P] {f : γ → G} {g : γ → P},
  Monotone f → Monotone g → Monotone fun x => f x +ᵥ g x
Defined in
Mathlib.Algebra.Order.AddTorsor
Cited by
1 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
PreorderPreorderPreorderVAddIsOrderedVAdd
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Around this declaration

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

Set.IsPWO.vadd · cited by 3IsPWO.vaddPreorder · cited by 7952PreorderLE.le.trans · cited by 3151le.transHVAdd.hVAdd · cited by 1820HVAdd.hVAddMonotone · cited by 1397MonotoneVAdd · cited by 616VAddIsOrderedVAdd · cited by 7IsOrderedVAddIsOrderedVAdd.vadd_le_vadd_left · cited by 4IsOrderedVAdd.vadd_le_vad…IsOrderedVAdd.vadd_le_vadd_right · cited by 4IsOrderedVAdd.vadd_le_vad…Monotone.vaddCITED BYCITES

Cites8

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Cited by1

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