Theorems · Theorem · group theory
AddSubmonoid.induction_of_closure_eq_top_right
∀ {M : Type u_1} [inst : AddMonoid M] {s : Set M} {motive : M → Prop},
AddSubmonoid.closure s = ⊤ → ∀ (x : M), motive 0 → (∀ (x y : M), y ∈ s → motive x → motive (x + y)) → motive x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement and proof · cited by 9,680
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- AddSubmonoid.mem_topproof · cited by 20
- AddSubmonoid.closure_induction_rightproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.