<style type="text/css">
ul.spaced li { padding-bottom: 1em; }
ul.empty li { list-style-type: none; }
+ tt { font-weight: bold; background-color: lightgray; }
+ tt.uri { font-weight: normal; background-color: transparent; }
</style>
</head>
<body>
<u>Examples:</u>
<ul class="empty">
<li> <tt>nat</tt> pattern matches
- <tt>cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt> only
+ <tt class="uri">cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt> only
</li>
<li> <tt>n?t</tt> pattern matches
- <tt>cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt> and
- <tt>cic:/Coq/Init/Logic/not.con</tt>
+ <tt class="uri">cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt> and
+ <tt class="uri">cic:/Coq/Init/Logic/not.con</tt>
</li>
<li> <tt>nat*</tt> pattern matches
- <tt>cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt>,
- <tt>cic:/Coq/Init/Peano/nat_case.con</tt> and many more
+ <tt class="uri">cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)</tt>,
+ <tt class="uri">cic:/Coq/Init/Peano/nat_case.con</tt> and many more
</li>
</ul>
</p>
</li>
<li>
- <b>hint</b>
+ <b>match <em><term></em></b>
+ <p>
+ <u>Examples:</u>
+ <ul class="empty">
+ <li> <tt>\forall x,y:nat.x+y=y+x</tt>
+ (commutativity of natural plus)
+ </li>
+ <li> <tt>\forall x,y,z:R.x*(y+z)=x*y+x*z</tt>
+ (distributivity of real times over real plus)
+ </li>
+ <li> <tt>nat \to nat \to nat</tt>
+ (all binary functions over naturals)
+ </li>
+ </ul>
+ </p>
</li>
<li>
- <b>match</b>
+ <b>hint <em><term></em></b>
+ <p>
+ <u>Examples:</u>
+ <ul class="empty">
+ <li> <tt>\forall n:nat. (fact n) = n * (fact (n - 1))</tt>
+ (how could we prove <em>n! = (n-1)! * n</em> ?)
+ </li>
+ <li> <tt>\forall n:nat.n \lt n+5</tt>
+ (how could we prove <em>n < n + 5</em> ?)
+ </li>
+ <li> <tt>\forall x,y:nat. x*y \lt (S x)*(S y)</tt>
+ (how could we prove <em>x*y < (x+1)*(y+1)</em> ?)
+ </li>
+ </ul>
+ </p>
</li>
<li>
- <b>elim</b>
+ <b>elim <em><identifier></em></b>
+ <p>
+ <u>Examples:</u>
+ <ul class="empty">
+ <li> <tt>nat</tt>
+ (induction/elimination principles over natural numbers)
+ </li>
+ <li> <tt>list</tt>
+ (induction/elimination principles over lists)
+ </li>
+ </ul>
+ </p>
</li>
</ul>
</td>