Theorems · Theorem · number theory
ModularGroup.exists_smul_mem_fd
∀ (z : UpperHalfPlane), ∃ g, g • z ∈ ModularGroup.fd
First Fundamental Domain Lemma: Any z : ℍ can be moved to 𝒟 by an element of
SL(2,ℤ)
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- UpperHalfPlanestatement and proof · cited by 626
- lt_of_not_geproof · cited by 374
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
- SemigroupAction.mul_smulproof · cited by 291
- UpperHalfPlane.coeproof · cited by 288
Cited by2
Results whose statement or proof uses this declaration.
- ModularGroup.exists_bound_of_invariant_of_isBigOproof · cited by 2
- ModularGroup.exists_one_half_le_im_smulproof · cited by 1