{α : Type u_4} →
  {β : Type u_5} →
    {r : α → α → Prop} →
      {s : β → β → Prop} →
        {P : Sort u} →
          {toRelEmbedding : r ↪r s} →
            {mem_range_of_rel' : ∀ (a : α) (b : β), s b (toRelEmbedding a) → b ∈ Set.range ⇑toRelEmbedding} →
              {toRelEmbedding' : r ↪r s} →
                {mem_range_of_rel'' : ∀ (a : α) (b : β), s b (toRelEmbedding' a) → b ∈ Set.range ⇑toRelEmbedding'} →
                  { toRelEmbedding := toRelEmbedding, mem_range_of_rel' := mem_range_of_rel' } =
                      { toRelEmbedding := toRelEmbedding', mem_range_of_rel' := mem_range_of_rel'' } →
                    (toRelEmbedding ≍ toRelEmbedding' → P) → P