Theorems · Theorem · order theory
IsSquare.nonneg
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : LinearOrder R] [ExistsAddOfLE R] [PosMulMono R] [AddLeftMono R] {x : R},
IsSquare x → 0 ≤ x- Defined in
- Mathlib.Algebra.Order.Ring.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- PosMulMonostatement and proof · cited by 165
- IsSquarestatement and proof · cited by 132
- mul_self_nonnegproof · cited by 35
Cited by4
Results whose statement or proof uses this declaration.
- IsSumSq.nonnegproof · cited by 2
- IsRealClosed.nonneg_iff_isSquareproof · cited by 1
- Real.isSquare_iffproof · cited by 0
- not_isSquare_of_negproof · cited by 0