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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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="c3">F1</font>, <font color="Maroon" title="c4">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>assume </b><a NAME="E1:12"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c3">F1</font> <a href="functor2.html#R1" title="FUNCTOR2:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">t</font> be    <a href="functor2.html#M1" title="FUNCTOR2:mode.1">transformation</a> of <font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">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/><a NAME="E1:12_1"/><i><font color="Green" title="E12">A2</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#D1" target="_self" title="FUNCTOR2:def.1">Def1</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#D5" target="_self" title="FUNCTOR2:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T6" target="_self" title="FUNCTOR2:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="functor2.html#E1:12_1"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:12"/>
<span class="p1">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <font color="Maroon" title="c5">t</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">t</font>
 <b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#T5" target="_self" title="FUNCTOR2:th.5">Th5</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">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/><a NAME="E1:12_2"/><i><font color="Green" title="E12">A3</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#D1" target="_self" title="FUNCTOR2:def.1">Def1</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F1</font></span>)</span></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span>
<b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#D5" target="_self" title="FUNCTOR2:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T6" target="_self" title="FUNCTOR2:th.6">Th6</a></i>
<br/>.= 
<font color="Maroon" title="c5">t</font> <a href="functor2.html#K2" title="FUNCTOR2:func.2">!</a> <font color="Maroon" title="c6">a</font>
<b>by </b><i><a class="txt" href="functor2.html#E1:12_2"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:12"/>
<font color="Maroon" title="c5">t</font> <a href="functor2.html#K3" title="FUNCTOR2:func.3">`*`</a> <span class="p1">(<span class="default"><a href="functor2.html#K1" title="FUNCTOR2:func.1">idt</a> <font color="Maroon" title="c3">F1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">t</font>
 <b>by </b><i><a class="txt" href="functor2.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor2.html#T5" target="_self" title="FUNCTOR2:th.5">Th5</a></i>;<br/>


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