Theorems · Theorem · order theory
two_mul_le_add_of_sq_eq_mul
Deprecated since 2026-04-20Use two_mul_le_add_of_sq_le_mul instead.
∀ {R : Type u} [inst : CommSemiring R] [inst_1 : LinearOrder R] [ExistsAddOfLE R] [MulPosStrictMono R]
[PosMulStrictMono R] [AddLeftReflectLE R] [AddLeftMono R] {a b r : R}, 0 ≤ a → 0 ≤ b → r ^ 2 = a * b → 2 * r ≤ a + b- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- LinearOrderstatement and proof · cited by 8,572
- AddLeftMonostatement and proof · cited by 687
- Eq.leproof · cited by 605
- ExistsAddOfLEstatement and proof · cited by 330
- PosMulStrictMonostatement and proof · cited by 151
- AddLeftReflectLEstatement and proof · cited by 119
- MulPosStrictMonostatement and proof · cited by 94
- two_mul_le_add_of_sq_le_mulproof · cited by 2
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