Theorems · Theorem · order theory
nonneg_le_nonneg_of_sq_le_sq
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [PosMulStrictMono R] [MulPosMono R] {a b : R},
0 ≤ b → a * a ≤ b * b → a ≤ b- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 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
- le_of_not_gtproof · cited by 430
- LT.lt.not_geproof · cited by 305
- PosMulStrictMonostatement and proof · cited by 151
- MulPosMonostatement and proof · cited by 128
- mul_self_lt_mul_selfproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- mul_self_le_mul_self_iffproof · cited by 7
- NonUnitalStarAlgHom.nnnorm_apply_leproof · cited by 2
- two_mul_le_add_of_sq_le_mulproof · cited by 2
- exists_norm_eq_iInf_of_complete_convexproof · cited by 1
- norm_eq_iInf_iff_real_inner_le_zeroproof · cited by 1
- InnerProductSpace.Core.norm_inner_le_normproof · cited by 1