Theorems · Theorem · order theory
inf_eq_half_smul_add_sub_abs_sub
∀ (R : Type u_2) {M : Type u_3} [inst : Semiring R] [inst_1 : Invertible 2] [inst_2 : Lattice M]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [IsOrderedAddMonoid M] (x y : M), x ⊓ y = ⅟2 • (x + y - |y - x|)- Defined in
- Mathlib.Algebra.Order.Module.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 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.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- absstatement · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- one_smulproof · cited by 1,374
- Latticestatement and proof · cited by 916
- Invertiblestatement and proof · cited by 549
- smul_smulproof · cited by 360
- Invertible.invOfstatement and proof · cited by 268
- two_smulproof · cited by 57
- invOf_mul_selfproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- inf_eq_half_smul_add_sub_abs_sub'proof · cited by 1