Theorems · Theorem · order theory
sq_pos_iff
∀ {R : Type u_3} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [ExistsAddOfLE R] {a : R},
0 < a ^ 2 ↔ a ≠ 0- Defined in
- Mathlib.Algebra.Order.Ring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- ExistsAddOfLEstatement and proof · cited by 330
- two_ne_zeroproof · cited by 251
- even_twoproof · cited by 17
- Even.pow_pos_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- sq_pos_of_ne_zeroproof · cited by 9
- NNReal.sqrt_mul_lt_half_add_of_neproof · cited by 1
- EuclideanGeometry.tendsto_inversion_nhdsNE_center_coboundedproof · cited by 0