∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} {inst : CommRing R} {inst_1 : CommRing S} {inst_2 : Algebra R S}
  {toGenerators : Algebra.Generators R S ι} {relation : σ → toGenerators.Ring}
  {span_range_relation_eq_ker : Ideal.span (Set.range relation) = toGenerators.ker}
  {toGenerators_1 : Algebra.Generators R S ι} {relation_1 : σ → toGenerators_1.Ring}
  {span_range_relation_eq_ker_1 : Ideal.span (Set.range relation_1) = toGenerators_1.ker},
  { toGenerators := toGenerators, relation := relation, span_range_relation_eq_ker := span_range_relation_eq_ker } =
      { toGenerators := toGenerators_1, relation := relation_1,
        span_range_relation_eq_ker := span_range_relation_eq_ker_1 } →
    toGenerators = toGenerators_1 ∧ relation = relation_1