Theorems · Theorem · order theory
sq_le_sq
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a b : α}, a ^ 2 ≤ b ^ 2 ↔ |a| ≤ |b|- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 30 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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement and proof · cited by 1,814
- abs_nonnegproof · cited by 168
- sq_absproof · cited by 49
- sq_le_sq₀proof · cited by 8
Cited by16
Results whose statement or proof uses this declaration.
- one_le_sq_iff_one_le_absproof · cited by 3
- Pell.IsFundamental.x_mul_y_le_y_mul_xproof · cited by 3
- abs_le_of_sq_le_sqproof · cited by 2
- Real.abs_sin_le_absproof · cited by 2
- Complex.norm_le_sqrt_two_mul_maxproof · cited by 2
- ModularGroup.isCompact_truncatedFundamentalDomainproof · cited by 1
- GaussianFourier.verticalIntegral_norm_leproof · cited by 1
- Pell.IsFundamental.y_le_yproof · cited by 1
- Real.sum_range_sub_log_div_leproof · cited by 1
- SzemerediRegularity.add_div_le_sum_sq_div_cardproof · cited by 1
- GaussianInt.normSq_le_normSq_of_re_le_of_im_leproof · cited by 1