Theorems · Theorem · order theory
abs_sub_lt_of_nonneg_of_lt
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] {a b n : G},
0 ≤ a → a < n → 0 ≤ b → b < n → |a - b| < n|a - b| < n if 0 ≤ a < n and 0 ≤ b < n.
- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- absstatement · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- sub_lt_iff_lt_addproof · cited by 39
- abs_sub_lt_iffproof · cited by 8
- lt_add_of_lt_of_nonnegproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Int.natAbs_coe_sub_coe_lt_of_ltproof · cited by 0