Theorems · Theorem · order theory
iUnion_Ioc_add_zsmul
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] [Archimedean α] {p : α},
0 < p → ∀ (a : α), ⋃ n, Set.Ioc (a + n • p) (a + (n + 1) • p) = Set.univ- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Set.univstatement · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- one_smulproof · cited by 1,374
- Set.Iocstatement · cited by 971
- add_assocproof · cited by 746
- Archimedeanstatement and proof · cited by 603
- Set.mem_iUnionproof · cited by 212
- add_smulproof · cited by 204
Cited by3
Results whose statement or proof uses this declaration.
- iUnion_Icc_add_zsmulproof · cited by 2
- iUnion_Ioc_add_intCastproof · cited by 2
- iUnion_Ioc_zsmulproof · cited by 0