Theorems · Theorem · group theory
FixedDetMatrices.reduce_of_not_pos
∀ {m : ℤ} {A : FixedDetMatrix (Fin 2) ℤ m},
↑A 1 0 = 0 →
¬0 < ↑A 0 0 →
FixedDetMatrices.reduce A = ModularGroup.T ^ (-(-↑A 0 1 / -↑A 1 1)) • ModularGroup.S • ModularGroup.S • A- Cited by
- 2 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement · cited by 4,303
- neg_negproof · cited by 960
- Matrix.detstatement · cited by 665
- Matrix.SpecialLinearGroupstatement · cited by 348
- zpow_negproof · cited by 198
- ModularGroup.Tstatement and proof · cited by 48
- ModularGroup.Sstatement and proof · cited by 36
- FixedDetMatrixstatement and proof · cited by 19
- FixedDetMatrices.reduceStepproof · cited by 7
- FixedDetMatrices.reducestatement and proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- FixedDetMatrices.reduce_mem_repsproof · cited by 1
- FixedDetMatrices.induction_onproof · cited by 1