Theorems · Theorem · number theory
Zsqrtd.sqLe_mul
∀ {d x y z w : ℕ},
(Zsqrtd.SqLe x 1 y d → Zsqrtd.SqLe z 1 w d → Zsqrtd.SqLe (x * w + y * z) d (x * z + d * y * w) 1) ∧
(Zsqrtd.SqLe x 1 y d → Zsqrtd.SqLe w d z 1 → Zsqrtd.SqLe (x * z + d * y * w) 1 (x * w + y * z) d) ∧
(Zsqrtd.SqLe y d x 1 → Zsqrtd.SqLe z 1 w d → Zsqrtd.SqLe (x * z + d * y * w) 1 (x * w + y * z) d) ∧
(Zsqrtd.SqLe y d x 1 → Zsqrtd.SqLe w d z 1 → Zsqrtd.SqLe (x * w + y * z) d (x * z + d * y * w) 1)- Defined in
- Mathlib.NumberTheory.Zsqrtd.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
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.
- one_mulproof · cited by 2,841
- sub_nonneg_of_leproof · cited by 37
- Zsqrtd.SqLestatement and proof · cited by 14
- Int.ofNat_le_ofNat_of_leproof · cited by 6
- le_of_sub_nonnegproof · cited by 5
- Int.le_of_ofNat_le_ofNatproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Zsqrtd.nonneg_mulproof · cited by 1