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FreeSemigroup.recOnMul

{α : Type u} →
  {C : FreeSemigroup α → Sort l} →
    (x : FreeSemigroup α) →
      ((x : α) → C (FreeSemigroup.of x)) →
        ((x : α) → (y : FreeSemigroup α) → C (FreeSemigroup.of x) → C y → C (FreeSemigroup.of x * y)) → C x

Recursor for free semigroup using of and *.

Defined in
Mathlib.Algebra.Free
Cited by
3 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FreeSemigroup.hom_ext · cited by 2FreeSemigroup.hom_extFreeSemigroup.toFreeMonoid_ne_one · cited by 0FreeSemigroup.toFreeMonoi…FreeSemigroup.recOnPure · cited by 0FreeSemigroup.recOnPureFreeSemigroup.length_map · cited by 0FreeSemigroup.length_mapFreeSemigroup · cited by 43FreeSemigroupFreeSemigroup.of · cited by 20FreeSemigroup.ofFreeSemigroup.recOn · cited by 0FreeSemigroup.recOnFreeSemigroup.recOnMulCITED BYCITES

Cites3

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

Cited by4

Results whose statement or proof uses this declaration.