Theorems · Theorem · order theory
iUnion_Icc_add_intCast
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [Archimedean α] (a : α),
⋃ n, Set.Icc (a + ↑n) (a + ↑n + 1) = Set.univ- Defined in
- Mathlib.Algebra.Order.ToIntervalMod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Set.univstatement and proof · cited by 3,945
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Set.iUnionstatement and proof · cited by 2,483
- Set.Iccstatement and proof · cited by 1,702
- Archimedeanstatement and proof · cited by 603
- zero_lt_oneproof · cited by 598
- Int.cast_oneproof · cited by 371
- Int.cast_addproof · cited by 124
- zsmul_oneproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- iUnion_Icc_intCastproof · cited by 1