∀ {ringId : ℕ} {checkCoeffDvd : Bool} {ringId_1 : ℕ} {checkCoeffDvd_1 : Bool},
  { ringId := ringId, checkCoeffDvd := checkCoeffDvd } = { ringId := ringId_1, checkCoeffDvd := checkCoeffDvd_1 } →
    ringId = ringId_1 ∧ checkCoeffDvd = checkCoeffDvd_1