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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font>, <font color="Olive" title="b3">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="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b4">G1</font>, <font color="Olive" title="b5">G2</font>, <font color="Olive" title="b6">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="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><br/> for <font color="Olive" title="b7">s</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b4">G1</font>,<font color="Olive" title="b5">G2</font><br/> for <font color="Olive" title="b8">s1</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b5">G2</font>,<font color="Olive" title="b6">G3</font><br/> for <font color="Olive" title="b9">t</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font><br/> for <font color="Olive" title="b10">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Olive" title="b2">F2</font>,<font color="Olive" title="b3">F3</font>  st <font color="Olive" title="b1">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> &amp; <font color="Olive" title="b2">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b3">F3</font> &amp; <font color="Olive" title="b4">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b5">G2</font> &amp; <font color="Olive" title="b5">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b6">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b8">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Olive" title="b7">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b9">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b10">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b9">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font>, <font color="Maroon" title="c6">F3</font> be  <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="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">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="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font><br/> for <font color="Olive" title="b4">s</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/> for <font color="Olive" title="b5">s1</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font><br/> for <font color="Olive" title="b6">t</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b7">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>  st <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Olive" title="b1">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">G2</font> &amp; <font color="Olive" title="b2">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b3">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Olive" title="b4">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b6">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b7">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b6">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c7">G1</font>, <font color="Maroon" title="c8">G2</font>, <font color="Maroon" title="c9">G3</font> be  <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="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font><br/> for <font color="Olive" title="b2">s1</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font><br/> for <font color="Olive" title="b3">t</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b4">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>  st <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b4">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b3">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c10">s</font> be    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font> being   <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font><br/> for <font color="Olive" title="b2">t</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b3">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>  st <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b3">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b2">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c11">s1</font> be    <a href="functor2.html#M2" title="FUNCTOR2:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font><br/> for <font color="Olive" title="b2">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>  st <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b2">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b1">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c12">t</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t1</font> being   <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>  st <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Olive" title="b1">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c13">t1</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span> )</span><br/>

























<b>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font> )
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c7">G1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font>
 <b>and </b><br/><a NAME="E3:47"/><i><font color="Green" title="E26">A3</font></i>: 
<font color="Maroon" title="c8">G2</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span></span><br/>

<a NAME="E4:47"/><i><font color="Green" title="E27">A4</font></i>: 
( <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E1:47"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="functor3.html#E2:47"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="functor3.html#E3:47"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="functor2.html#D6" title="FUNCTOR2:def.6">FUNCTOR2:def 6</a></i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="ref" href="functor2.html#T4" title="FUNCTOR2:th.4">FUNCTOR2:4</a></i>;<br/>
<a NAME="E6:47"/><i><font color="Green" title="E29">A6</font></i>: 
( <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F3</font> &amp; <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E7:47"/>
<font color="Maroon" title="c7">G1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font>
 
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor2.html#T4" title="FUNCTOR2:th.4">FUNCTOR2:4</a></i>;<br/>
<a NAME="E8:47"/><b>then </b><i><font color="Green" title="E30">A7</font></i>: 
( <font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E9:47"/><i><font color="Green" title="E31">A8</font></i>: 
( <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c9">G3</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E10:47"/>
<font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R2" title="FUNCTOR2:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="txt" href="functor3.html#E1:47"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="functor3.html#E2:47"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="functor3.html#E32"><i><font color="Green" title="E21">Lm2</font></i></a></i>;<br/>
<a NAME="E11:47"/><b>then </b><i><font color="Green" title="E32">A9</font></i>: 
<font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="ref" href="functor2.html#D6" title="FUNCTOR2:def.6">FUNCTOR2:def 6</a></i>;<br/>
<a NAME="E12:47"/><i><font color="Green" title="E33">A10</font></i>: 
( <font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c13">t1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> &amp; <font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="functor3.html#E2:47"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="functor3.html#E3:47"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T22" target="_self" title="FUNCTOR3:th.22">Th22</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">t1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E2:47"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="functor3.html#E3:47"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="functor3.html#E5:47"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="functor3.html#T22" target="_self" title="FUNCTOR3:th.22">Th22</a>, <a class="ref" href="functor2.html#T10" title="FUNCTOR2:th.10">FUNCTOR2:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K5" title="FUNCTOR2:func.5">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T13" target="_self" title="FUNCTOR3:th.13">Th13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E2:47"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="functor3.html#E3:47"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="functor2.html#D8" title="FUNCTOR2:def.8">FUNCTOR2:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T14" target="_self" title="FUNCTOR3:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E6:47"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="functor3.html#E8:47"><i><font color="Green" title="E30">A7</font></i></a>, <a class="ref" href="functor2.html#T8" title="FUNCTOR2:th.8">FUNCTOR2:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E6:47"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="functor3.html#E8:47"><i><font color="Green" title="E30">A7</font></i></a>, <a class="ref" href="functor2.html#T8" title="FUNCTOR2:th.8">FUNCTOR2:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E3:47"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="functor3.html#E4:47"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="functor3.html#T22" target="_self" title="FUNCTOR3:th.22">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E8:47"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="functor3.html#E9:47"><i><font color="Green" title="E31">A8</font></i></a>, <a class="ref" href="functor2.html#T8" title="FUNCTOR2:th.8">FUNCTOR2:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">s1</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c13">t1</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E6:47"><i><font color="Green" title="E29">A6</font></i></a>, <a class="txt" href="functor3.html#E9:47"><i><font color="Green" title="E31">A8</font></i></a>, <a class="txt" href="functor3.html#E11:47"><i><font color="Green" title="E32">A9</font></i></a>, <a class="txt" href="functor3.html#E12:47"><i><font color="Green" title="E33">A10</font></i></a>, <a class="ref" href="functor2.html#T8" title="FUNCTOR2:th.8">FUNCTOR2:8</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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