Theorems · Theorem · group theory
Finset.sum_erase_lt_of_pos
∀ {ι : Type u_1} {κ : Type u_5} [inst : DecidableEq ι] [inst_1 : AddCommMonoid κ] [inst_2 : LT κ] [AddLeftStrictMono κ]
{s : Finset ι} {d : ι}, d ∈ s → ∀ {f : ι → κ}, 0 < f d → ∑ m ∈ s.erase d, f m < ∑ m ∈ s, f m- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.erasestatement and proof · cited by 455
- AddLeftStrictMonostatement and proof · cited by 203
- Finset.sum_insertproof · cited by 196
- Finset.insert_eraseproof · cited by 65
- Finset.notMem_eraseproof · cited by 59
- lt_add_of_pos_leftproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- card_addOrderOf_eq_totient_aux₂proof · cited by 2
- card_orderOf_eq_totient_aux₂proof · cited by 2