Theorems · Theorem · order theory
sup_sub_inf_eq_abs_sub
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddCommGroup α] [AddLeftMono α] (a b : α), a ⊔ b - a ⊓ b = |b - a|- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
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.
- AddCommGroupstatement and proof · cited by 12,871
- absstatement and proof · cited by 1,814
- sub_selfproof · cited by 996
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- neg_subproof · cited by 272
- abs_nonnegproof · cited by 168
- sup_commproof · cited by 165
- sup_eq_leftproof · cited by 71
- sup_idemproof · cited by 29
- sup_sup_sup_commproof · cited by 12
- sub_infproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- abs_sub_sup_add_abs_sub_infproof · cited by 2
- two_nsmul_inf_eq_add_sub_abs_subproof · cited by 1
- two_nsmul_sup_eq_add_add_abs_subproof · cited by 1