Theorems · Theorem · order theory
abs_sub_le_max_sub
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] {a b c : G},
a ≤ b → b ≤ c → ∀ (d : G), |b - d| ≤ max (c - d) (d - a)- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- neg_subproof · cited by 272
- sub_nonnegproof · cited by 167
- abs_of_nonposproof · cited by 53
- sub_le_sub_leftproof · cited by 43
- le_max_of_le_leftproof · cited by 31
- le_max_of_le_rightproof · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- ODE.FunSpace.mem_closedBallproof · cited by 3
- ODE.FunSpace.dist_iterate_next_iterate_next_leproof · cited by 2