Theorems · Theorem · order theory
Set.Icc_add_Icc
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] [AddLeftReflectLE α]
[ExistsAddOfLE α] {a b c d : α}, a ≤ b → c ≤ d → Set.Icc a b + Set.Icc c d = Set.Icc (a + c) (b + d)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccstatement and proof · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- add_assocproof · cited by 746
- LE.le.antisymmproof · cited by 507
- Set.addstatement · cited by 338
- ExistsAddOfLEstatement and proof · cited by 330
- le_totalproof · cited by 294
- AddLeftReflectLEstatement and proof · cited by 119
- add_right_commproof · cited by 85
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