Theorems · Theorem · group theory

FreeAbelianGroup.induction_on

∀ {α : Type u} {motive : FreeAbelianGroup α → Prop} (z : FreeAbelianGroup α),
  motive 0 →
    (∀ (x : α), motive (FreeAbelianGroup.of x)) →
      (∀ (x : α), motive (FreeAbelianGroup.of x) → motive (-FreeAbelianGroup.of x)) →
        (∀ (x y : FreeAbelianGroup α), motive x → motive y → motive (x + y)) → motive z

Defined in

Mathlib.GroupTheory.FreeAbelianGroup

Cited by

5 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound