Theorems · Theorem · number theory
UpperHalfPlane.normSq_pos
∀ (z : UpperHalfPlane), 0 < Complex.normSq ↑z
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement · cited by 5,565
- MonoidWithZeroHomstatement · cited by 704
- UpperHalfPlanestatement and proof · cited by 626
- UpperHalfPlane.coestatement · cited by 288
- Complex.normSqstatement · cited by 103
- Complex.normSq_posproof · cited by 7
- UpperHalfPlane.ne_zeroproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- UpperHalfPlane.im_inv_neg_coe_posproof · cited by 7
- ModularGroup.im_lt_im_S_smulproof · cited by 1
- UpperHalfPlane.im_pnat_div_posproof · cited by 0
- ModularGroup.normSq_S_smul_lt_oneproof · cited by 0
- UpperHalfPlane.normSq_ne_zeroproof · cited by 0