Theorems · Theorem · order theory

iUnion_Icc_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.Icc (a + n • p) (a + (n + 1) • p) = Set.univ

Defined in

Mathlib.Algebra.Order.ToIntervalMod

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean