Theorems · Theorem · order theory
sup_div_inf_eq_mabs_div
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : CommGroup α] [MulLeftMono α] (a b : α), (a ⊔ b) / (a ⊓ b) = |b / a|ₘ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeCommGroupMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommGroupstatement and proof · cited by 990
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- sup_commproof · cited by 165
- mabsstatement and proof · cited by 148
- inv_divproof · cited by 92
- sup_eq_leftproof · cited by 71
- sup_idemproof · cited by 29
- div_self'proof · cited by 25
- sup_sup_sup_commproof · cited by 12
- one_le_mabsproof · cited by 11
- sup_divproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- mabs_div_sup_mul_mabs_div_infproof · cited by 2
- inf_sq_eq_mul_div_mabs_divproof · cited by 0
- sup_sq_eq_mul_mul_mabs_divproof · cited by 0