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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>, <font color="Maroon" title="c4">D</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c5">F1</font>, <font color="Maroon" title="c6">F2</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>;<br/><b>let </b><font color="Maroon" title="c7">G1</font>, <font color="Maroon" title="c8">G2</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>;<br/><b>let </b><font color="Maroon" title="c9">H1</font>, <font color="Maroon" title="c10">H2</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="c3">C</font>,<font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c11">t</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c5">F1</font>,<font color="Maroon" title="c6">F2</font>;<br/><b>let </b><font color="Maroon" title="c12">s</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font>;<br/><b>let </b><font color="Maroon" title="c13">u</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c9">H1</font>,<font color="Maroon" title="c10">H2</font>;<br/>























<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c5">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">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="c9">H1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c10">H2</font> )
 ;<br/>

<a NAME="E2:43"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
( <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c10">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <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">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font> )
 
<b>by </b><i><a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E3:43"/><b>then </b><i><font color="Green" title="E23">A3</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E1:43"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E4:43"/><i><font color="Green" title="E24">A4</font></i>: 
( <font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</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="c6">F2</font> &amp; <font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E1:43"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E5:43"/><i><font color="Green" title="E25">A5</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">F2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c13">u</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">s</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">F2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c11">t</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c11">t</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="functor3.html#E1:43"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="functor3.html#T15" target="_self" title="FUNCTOR3:th.15">Th15</a>, <a class="ref" href="functor3.html#T16" target="_self" title="FUNCTOR3:th.16">Th16</a>, <a class="ref" href="functor3.html#T17" target="_self" title="FUNCTOR3:th.17">Th17</a></i>;<br/>
<a NAME="E6:43"/><i><font color="Green" title="E26">A6</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="functor0.html#T33" title="FUNCTOR0:th.33">FUNCTOR0:33</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c12">s</font></span>)</span> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c11">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">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="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c12">s</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">F2</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="c9">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c11">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E2:43"><i><font color="Green" title="E22">A2</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="c13">u</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">F2</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="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">F2</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="c9">H1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="functor3.html#K5" title="FUNCTOR3:func.5">*</a> <font color="Maroon" title="c11">t</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E3:43"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="functor3.html#E5:43"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="functor3.html#E6:43"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="functor2.html#T8" title="FUNCTOR2:th.8">FUNCTOR2:8</a></i>
<br/>.= 
<font color="Maroon" title="c13">u</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">s</font> <a href="functor3.html#K7" title="FUNCTOR3:func.7">(#)</a> <font color="Maroon" title="c11">t</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E4:43"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="functor3.html#T13" target="_self" title="FUNCTOR3:th.13">Th13</a></i>
;<br/>


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