Theorems · Theorem · order theory
abs_mul_self
∀ {α : Type u_1} [inst : Ring α] [inst_1 : LinearOrder α] [IsOrderedRing α] (a : α), |a * a| = a * a- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- 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
- abs_mulproof · cited by 98
- abs_mul_abs_selfproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- abs_sqproof · cited by 4
- Real.cos_pos_of_le_oneproof · cited by 2