Theorems · Theorem · group theory

Monoid.CoprodI.induction_on

∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] {motive : Monoid.CoprodI M → Prop}
  (m : Monoid.CoprodI M),
  motive 1 →
    (∀ (i : ι) (m : M i), motive (Monoid.CoprodI.of m)) →
      (∀ (x y : Monoid.CoprodI M), motive x → motive y → motive (x * y)) → motive m

Defined in: Mathlib.GroupTheory.CoprodI
Cited by: 3 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid

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Cites6

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

DFunLike.coestatement and proof · cited by 62,936
Monoidstatement and proof · cited by 3,887
MonoidHomstatement · cited by 3,629
Monoid.CoprodIstatement and proof · cited by 52
Monoid.CoprodI.ofstatement and proof · cited by 45
Monoid.CoprodI.induction_leftproof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

Monoid.PushoutI.induction_onproof · cited by 1
Monoid.CoprodI.Word.prod_smulproof · cited by 1
Monoid.CoprodI.lift_range_leproof · cited by 1