Theorems · Theorem · group theory

Submonoid.closure_induction_left

∀ {M : Type u_1} [inst : Monoid M] {s : Set M} {motive : (m : M) → m ∈ Submonoid.closure s → Prop},
  motive 1 ⋯ →
    (∀ (x : M) (hx : x ∈ s) (y : M) (hy : y ∈ Submonoid.closure s), motive y hy → motive (x * y) ⋯) →
      ∀ {x : M} (h : x ∈ Submonoid.closure s), motive x h

Defined in

Mathlib.Algebra.Group.Submonoid.Membership

Cited by

4 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Monoid