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<b>let </b><font color="Maroon">C1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6" target="_self">strict</a> <a href="altcat_1.html#V10" target="_self">pseudo-functional</a>  <a href="altcat_1.html#L2" target="_self">AltCatStr</a> , <font color="Maroon">C2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6" target="_self">strict</a> <a href="altcat_1.html#V10" target="_self">pseudo-functional</a>  <a href="altcat_1.html#L2" target="_self">AltCatStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:41_1_2"/><i><font color="Green">E114</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E2:41_1_2"/><i><font color="Green">E115</font></i>: 
for <font color="Olive">a1</font>, <font color="Olive">a2</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font> holds  <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">a2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Olive">a1</font>,<font color="Olive">a2</font>
 <b>and </b><br/><a NAME="E3:41_1_2"/><i><font color="Green">E116</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:41_1_2"/><i><font color="Green">E117</font></i>: 
for <font color="Olive">a1</font>, <font color="Olive">a2</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C2</font> holds  <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">a2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Olive">a1</font>,<font color="Olive">a2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:41_1_2_1"/><i><font color="Green">E118</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><b>then reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">i</font>, <font color="Maroon">a2</font> = <font color="Maroon">j</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">b1</font> = <font color="Maroon">i</font>, <font color="Maroon">b2</font> = <font color="Maroon">j</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C2</font> <b>by </b><i>, </i>;<br/><b>thus </b>the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">C1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> = 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>

<br/>.= 
 <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
<b>by </b><i/>
<br/>.= 
the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">C2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>

;<br/></div><b>end;</b></div>
<a NAME="E6:41_1_2"/><b>then </b><i><font color="Green">E121</font></i>: 
the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1" target="_self">Arrows</a> of <font color="Maroon">C2</font>
 
<b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:41_1_2_2"/><i><font color="Green">E122</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><b>then reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">i</font>, <font color="Maroon">a2</font> = <font color="Maroon">j</font>, <font color="Maroon">a3</font> = <font color="Maroon">k</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">b1</font> = <font color="Maroon">i</font>, <font color="Maroon">b2</font> = <font color="Maroon">j</font>, <font color="Maroon">b3</font> = <font color="Maroon">k</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C2</font> <b>by </b><i>, </i>;<br/><a NAME="E4:41_1_2_2"/><i><font color="Green">E124</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">a3</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">b3</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E5:41_1_2_2"/>
<span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>
 <b>by </b><i/>;<br/><b>hence </b>the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">C1</font> <a href="multop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="altcat_1.html#K6" target="_self">FuncComp</a> <span class="p2">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font></span>)</span>,<span class="p2">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">b3</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1" target="_self">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="altcat_1.html#K1" target="_self">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, </i>
<br/>.= 
the <a href="altcat_1.html#U2" target="_self">Comp</a> of <font color="Maroon">C2</font> <a href="multop_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:41_1_2"/>
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font>
 <b>by </b><i>, , , </i>;<br/>


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