Theorems · Theorem · order theory
mul_self_inj
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [PosMulStrictMono R] [MulPosMono R] {a b : R},
0 ≤ a → 0 ≤ b → (a * a = b * b ↔ a = b)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- PosMulStrictMonostatement and proof · cited by 151
- MulPosMonostatement and proof · cited by 128
- StrictMonoOn.eq_iff_eqproof · cited by 3
- strictMonoOn_mul_selfproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpointproof · cited by 1
- abs_eq_iff_mul_self_eqproof · cited by 1