Theorems · Theorem · group theory

AddSubmonoid.induction_of_closure_eq_top_left

∀ {M : Type u_1} [inst : AddMonoid M] {s : Set M} {motive : M → Prop},
  AddSubmonoid.closure s = ⊤ → ∀ (x : M), motive 0 → (∀ x ∈ s, ∀ (y : M), motive y → motive (x + y)) → motive x

Defined in

Mathlib.Algebra.Group.Submonoid.Membership

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoid