Theorems · Theorem · order theory
abs_one
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsOrderedRing α], |1| = 1- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- RingLinearOrderIsOrderedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- absstatement · cited by 1,814
- IsOrderedRingstatement and proof · cited by 777
- zero_le_oneproof · cited by 316
- abs_of_nonnegproof · cited by 279
Cited by88
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- ModularForm.SL_slash_applyproof · cited by 7
- ModularGroup.im_smul_eq_div_normSqproof · cited by 6
- Affine.Simplex.ExcenterExists.dist_excenterproof · cited by 6
- absHomproof · cited by 5
- Real.exp_one_near_10proof · cited by 4
- HasFDerivAt.hasFDerivAt_norm_smulproof · cited by 4
- one_le_sq_iff_one_le_absproof · cited by 3
- ArchimedeanClass.exists_nat_ge_of_mk_nonnegproof · cited by 3
- Real.abs_sinc_le_oneproof · cited by 3
- Polynomial.Chebyshev.eval_T_real_eq_neg_one_iffproof · cited by 3
- Polynomial.Chebyshev.eval_T_real_eq_one_iffproof · cited by 3