Theorems · Theorem · order theory
Finset.sum_eq_sum_iff_of_le
∀ {ι : Type u_9} {M : Type u_10} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M]
{s : Finset ι} {f g : ι → M}, (∀ i ∈ s, f i ≤ g i) → (∑ i ∈ s, f i = ∑ i ∈ s, g i ↔ ∀ i ∈ s, f i = g i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, 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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement and proof · cited by 5,195
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- Finset.sum_insertproof · cited by 196
- Finset.sum_le_sumproof · cited by 182
- Finset.induction_onproof · cited by 167
- Finset.mem_insert_selfproof · cited by 128
- Finset.mem_insert_of_memproof · cited by 109
- Finset.notMem_emptyproof · cited by 40
- Finset.forall_mem_insertproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Configuration.HasLines.lineCount_eq_pointCountproof · cited by 3
- Configuration.HasLines.exists_bijective_of_card_eqproof · cited by 1