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Theorems · Theorem · number theory

Zsqrtd.nonnegg_neg_pos

∀ {c d a b : ℕ}, Zsqrtd.Nonnegg c d (-↑a) ↑b ↔ Zsqrtd.SqLe a d b c
Defined in
Mathlib.NumberTheory.Zsqrtd.Basic
Cited by
6 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Zsqrtd.nonnegg_pos_neg · cited by 5Zsqrtd.nonnegg_pos_negZsqrtd.nonneg_add_lem · cited by 1Zsqrtd.nonneg_add_lemZsqrtd.nonneg_mul · cited by 1Zsqrtd.nonneg_mulZsqrtd.nonneg_muld · cited by 1Zsqrtd.nonneg_muldZsqrtd.nonneg_smul · cited by 1Zsqrtd.nonneg_smulZsqrtd.Nonneg.add · cited by 1Nonneg.addMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroNat.cast_zero · cited by 1870Nat.cast_zeroneg_zero · cited by 542neg_zeroZsqrtd.SqLe · cited by 14Zsqrtd.SqLeZsqrtd.Nonnegg · cited by 6Zsqrtd.NonneggZsqrtd.nonnegg_neg_posCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.