Theorems · Theorem · number theory
ModularGroup.bottom_row_surj
∀ {R : Type u_1} [inst : CommRing R], Set.SurjOn (fun g => ↑g 1) Set.univ {cd | IsCoprime (cd 0) (cd 1)}Every pair ![c, d] of coprime integers is the "bottom row" of some element g=[[*,*],[c,d]]
of SL(2,ℤ).
- Defined in
- Mathlib.NumberTheory.Modular
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Set.ofPredstatement and proof · cited by 6,101
- Matrixstatement and proof · cited by 4,303
- Set.univstatement · cited by 3,945
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- Matrix.detstatement and proof · cited by 665
- neg_mulproof · cited by 654
- Set.mem_univproof · cited by 416
- Matrix.SpecialLinearGroupstatement · cited by 348
- Matrix.ofproof · cited by 336
Cited by2
Results whose statement or proof uses this declaration.
- ModularGroup.exists_max_improof · cited by 1
- ModularGroup.exists_row_one_eq_and_min_reproof · cited by 1