equal
deleted
inserted
replaced
734 |
734 |
735 In case the goal is an implication, induction does one more thing: the |
735 In case the goal is an implication, induction does one more thing: the |
736 proposition to be proved in each case is not the whole implication but only |
736 proposition to be proved in each case is not the whole implication but only |
737 its conclusion; the premises of the implication are immediately made |
737 its conclusion; the premises of the implication are immediately made |
738 assumptions of that case. That is, if in the above proof we replace |
738 assumptions of that case. That is, if in the above proof we replace |
739 \isacom{show}~@{text"P(n)"} by |
739 \isacom{show}~@{text"\"P(n)\""} by |
740 \mbox{\isacom{show}~@{text"A(n) \<Longrightarrow> P(n)"}} |
740 \mbox{\isacom{show}~@{text"\"A(n) \<Longrightarrow> P(n)\""}} |
741 then \isacom{case}~@{text 0} stands for |
741 then \isacom{case}~@{text 0} stands for |
742 \begin{quote} |
742 \begin{quote} |
743 \isacom{assume} \ @{text"0: \"A(0)\""}\\ |
743 \isacom{assume} \ @{text"0: \"A(0)\""}\\ |
744 \isacom{let} @{text"?case = \"P(0)\""} |
744 \isacom{let} @{text"?case = \"P(0)\""} |
745 \end{quote} |
745 \end{quote} |