Theorems · Theorem · order theory
inf_add_sup
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddCommGroup α] [AddLeftMono 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
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.
- AddCommGroupstatement and proof · cited by 12,871
- add_commproof · cited by 1,535
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- sup_commproof · cited by 165
- neg_add_cancel_rightproof · cited by 75
- add_neg_cancel_rightproof · cited by 65
- add_neg_cancel_commproof · cited by 14
- add_supproof · cited by 6
- neg_infproof · cited by 4
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