Theorems · Theorem · number theory
ModularGroup.exists_one_half_le_im_smul
∀ (τ : UpperHalfPlane), ∃ γ, 1 / 2 ≤ (γ • τ).im
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- UpperHalfPlanestatement and proof · cited by 626
- le_of_not_gtproof · cited by 430
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
- UpperHalfPlane.imstatement and proof · cited by 128
- UpperHalfPlane.im_posproof · cited by 62
- mul_pos_of_neg_of_negproof · cited by 40
- ModularGroup.fdproof · cited by 17
- ModularGroup.exists_smul_mem_fdproof · cited by 2
- ModularGroup.three_le_four_mul_im_sq_of_mem_fdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ModularGroup.exists_one_half_le_im_smul_and_norm_denom_leproof · cited by 1