src/Doc/ProgProve/Isar.thy
changeset 49837 007f03af6c6a
parent 48985 5386df44a037
child 51443 4edb82207c5c
equal deleted inserted replaced
49832:2af09163cba1 49837:007f03af6c6a
   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}