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Theorems · Theorem · order theory

le_abs

∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] {a b : α}, a ≤ |b| ↔ a ≤ b ∨ a ≤ -b
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Abs
Cited by
5 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupLinearOrder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.sub_le_dist · cited by 2Real.sub_le_distEuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one · cited by 1Sphere.inter_orthRadius_e…le_abs' · cited by 1le_abs'ContinuousMap.apply_le_norm · cited by 0ContinuousMap.apply_le_no…Polynomial.Chebyshev.isExtrOn_T_real_iff · cited by 0Chebyshev.isExtrOn_T_real…LinearOrder · cited by 8572LinearOrderAddGroup · cited by 4410AddGroupabs · cited by 1814absle_max_iff · cited by 26le_max_iffle_absCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.