Mathlib Map

Theorems · Theorem · field theory

IsSquare.of_nonneg

∀ {R : Type u} [inst : Field R] [IsRealClosed R] [inst_2 : LinearOrder R] [IsStrictOrderedRing R] {x : R},
  0 ≤ x → IsSquare x

Alias of the forward direction of IsRealClosed.nonneg_iff_isSquare.

Defined in
Mathlib.FieldTheory.IsRealClosed.Basic
Cited by
2 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldIsRealClosedLinearOrderIsStrictOrderedRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsRealClosed.exists_eq_pow_of_nonneg · cited by 0IsRealClosed.exists_eq_po…IsRealClosed.exists_eq_zpow_of_nonneg · cited by 0IsRealClosed.exists_eq_zp…LinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingIsSquare · cited by 132IsSquareIsRealClosed · cited by 13IsRealClosedIsRealClosed.nonneg_iff_isSquare · cited by 1IsRealClosed.nonneg_iff_i…IsSquare.of_nonnegCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.