Theorems · Theorem · order theory
Finset.sum_sdiff_lt_sum_sdiff
∀ {ι : Type u_9} {M : Type u_10} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M]
[inst_3 : DecidableEq ι] {s t : Finset ι} {f : ι → M},
∑ i ∈ s \ t, f i < ∑ i ∈ t \ s, f i ↔ ∑ i ∈ s, f i < ∑ i ∈ t, f i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Disjointproof · cited by 2,201
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- add_lt_add_iff_rightproof · cited by 42
- Finset.sum_unionproof · cited by 40
- Finset.inter_commproof · cited by 25
- Finset.sdiff_union_interproof · cited by 9
- Finset.disjoint_sdiff_interproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Finset.geomSum_ofColex_strictMonoproof · cited by 2