Theorems · Theorem · order theory
abs_eq_iff_mul_self_eq
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a b : α}, |a| = |b| ↔ a * a = b * b- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 1 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
- abs_mul_abs_selfproof · cited by 21
- mul_self_injproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Int.natAbs_eq_iff_mul_self_eqproof · cited by 1