Before revision: Weakening the hypothesis results in the stronger principle that any real number which is not equal or below some non-positive number is positive, Elevating the De Morgan's law for to an equivalence, as is the case in classical logic, the preivous statement already implies this.
After revision: Weakening the antecedent results in the stronger principle that any real number which is not equal or below some non-positive number is positive, Elevating the De Morgan's law for to an equivalence, as is the case in classical logic, the preivous statement already implies this.