Theorems · Theorem · order theory
inf_mul_sup
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : CommGroup α] [MulLeftMono α] (a b : α), (a ⊓ b) * (a ⊔ b) = a * b- Defined in
- Mathlib.Algebra.Order.Group.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeCommGroupMulLeftMono
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.
- mul_commproof · cited by 2,262
- CommGroupstatement and proof · cited by 990
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- sup_commproof · cited by 165
- inv_mul_cancel_rightproof · cited by 70
- mul_inv_cancel_rightproof · cited by 53
- mul_inv_cancel_commproof · cited by 13
- mul_supproof · cited by 6
- inv_infproof · cited by 3
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