Theorems · Theorem · logic and foundations
IsSemilinearSet.isProperSemilinearSet
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M} [IsCancelAdd M], IsSemilinearSet s → IsProperSemilinearSet sThe proper decomposition of semilinear sets: every semilinear set is a finite union of proper linear sets.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidIsCancelAdd
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.
- Setstatement and proof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Finiteproof · cited by 1,814
- Set.sUnionproof · cited by 392
- IsCancelAddstatement and proof · cited by 79
- Set.sUnion_eq_biUnionproof · cited by 51
- IsSemilinearSetstatement and proof · cited by 44
- IsLinearSetproof · cited by 28
- IsProperSemilinearSetstatement and proof · cited by 10
- IsProperSemilinearSet.biUnionproof · cited by 2
- IsLinearSet.isProperSemilinearSetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.isSemilinearSet_iff_ultimately_periodicproof · cited by 1