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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: FUNCTOR3:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font> being   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a><br/>  for <font color="Olive" title="b4">F1</font>, <font color="Olive" title="b5">F2</font>, <font color="Olive" title="b6">F3</font> being   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font><br/>  for <font color="Olive" title="b7">G1</font>, <font color="Olive" title="b8">G2</font>, <font color="Olive" title="b9">G3</font> being   <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>   <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font><br/>  for <font color="Olive" title="b10">s</font> being    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b7">G1</font>,<font color="Olive" title="b8">G2</font><br/>  for <font color="Olive" title="b11">s1</font> being    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b8">G2</font>,<font color="Olive" title="b9">G3</font><br/>  for <font color="Olive" title="b12">t</font> being    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Olive" title="b4">F1</font>,<font color="Olive" title="b5">F2</font><br/>  for <font color="Olive" title="b13">t1</font> being    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Olive" title="b5">F2</font>,<font color="Olive" title="b6">F3</font>  st <font color="Olive" title="b4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b5">F2</font> &amp; <font color="Olive" title="b5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b6">F3</font> &amp; <font color="Olive" title="b7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b8">G2</font> &amp; <font color="Olive" title="b8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Olive" title="b10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b13">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b12">t</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b12">t</font></span>)</span></div></div>
