Theorems · Theorem · number theory
ModularGroup.im_lt_im_S_smul
∀ {z : UpperHalfPlane}, Complex.normSq ↑z < 1 → z.im < (ModularGroup.S • z).imIf |z| < 1, then applying S strictly decreases im.
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Units.valproof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
- Complex.ofRealproof · cited by 1,654
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- MonoidWithZeroHomstatement · cited by 704
Cited by1
Results whose statement or proof uses this declaration.
- ModularGroup.exists_smul_mem_fdproof · cited by 2