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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E1">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: RINGCAT1:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/>  for <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>  st <font color="Olive" title="b4">f</font> is  <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a>  &amp; <font color="Olive" title="b5">g</font> is  <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a>  holds <br/><font color="Olive" title="b5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f</font> is  <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> </div></div>
