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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  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a> <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c5">F1</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="c6">G1</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="c7">H1</font>, <font color="Maroon" title="c8">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="c9">r</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c7">H1</font>,<font color="Maroon" title="c8">H2</font>;<br/>

















<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c7">H1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">H2</font>
 ;<br/>

<a NAME="E2:30"/><i><font color="Green" title="E15">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">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="c8">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="functor0.html#T33" title="FUNCTOR0:th.33">FUNCTOR0:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">m</font> = <font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span> as    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c7">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font> <b>by </b><i><a class="ref" href="functor0.html#T33" title="FUNCTOR0:th.33">FUNCTOR0:33</a></i>;<br/>
<a NAME="E4:30"/>
<font color="Maroon" title="c7">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c8">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G1</font>
 
<b>by </b><i><a class="txt" href="functor3.html#E1:30"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<a NAME="E5:30"/><b>then </b><i><font color="Green" title="E16">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">H1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">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="c8">H2</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font>
 
<b>by </b><i><a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c5">F1</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c11">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E1:30"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="functor3.html#T10" target="_self" title="FUNCTOR3:th.10">Th10</a>, <a class="ref" href="functor3.html#T12" target="_self" title="FUNCTOR3:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c9">r</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="functor3.html#E1:30"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="functor3.html#T12" target="_self" title="FUNCTOR3:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c9">r</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c11">a</font>
<b>by </b><i><a class="txt" href="functor3.html#E1:30"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="functor3.html#T12" target="_self" title="FUNCTOR3:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c10">m</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c11">a</font>
<b>by </b><i><a class="txt" href="functor3.html#E2:30"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="functor0.html#T33" title="FUNCTOR0:th.33">FUNCTOR0:33</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:30"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <font color="Maroon" title="c5">F1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c9">r</font> <a href="functor3.html#K6" title="FUNCTOR3:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c5">F1</font></span>)</span>
 <b>by </b><i><a class="txt" href="functor3.html#E5:30"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="functor2.html#T5" title="FUNCTOR2:th.5">FUNCTOR2:5</a></i>;<br/>


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