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Theorems · Theorem · logic and foundations

IsLinearSet.isSemilinearSet

∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsLinearSet s → IsSemilinearSet s
Defined in
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs
Cited by
10 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsSemilinearSet.image · cited by 9IsSemilinearSet.imageIsSemilinearSet.add · cited by 2IsSemilinearSet.addIsLinearSet.closure · cited by 1IsLinearSet.closureIsSemilinearSet.singleton · cited by 1IsSemilinearSet.singletonIsSemilinearSet.univ · cited by 1IsSemilinearSet.univIsSemilinearSet.closure_finset · cited by 1IsSemilinearSet.closure_f…IsSemilinearSet.exists_fg_eq_subtypeVal · cited by 1IsSemilinearSet.exists_fg…IsSemilinearSet.of_fg · cited by 0IsSemilinearSet.of_fgIsSemilinearSet.vadd · cited by 0IsSemilinearSet.vaddIsSemilinearSet.closure_of_finite · cited by 0IsSemilinearSet.closure_o…Set · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidIsSemilinearSet · cited by 44IsSemilinearSetIsLinearSet · cited by 28IsLinearSetSet.sUnion_singleton · cited by 17Set.sUnion_singletonIsLinearSet.isSemilinearSetCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.