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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>













<b>assume </b><a NAME="E1:23"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D1">FUNCTOR2:def 1</a><br/>

<b>assume </b><a NAME="E2:23"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> holds <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D1">FUNCTOR2:def 1</a><br/>

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D1">FUNCTOR2:def 1</a><br/>

<a NAME="E3:23"/><i><font color="Green">E9</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="functor0.html#T34">FUNCTOR0:34</a></i>;<br/>
<a NAME="E4:23"/><i><font color="Green">E10</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="functor3.html#E2:23"><i><font color="Green">E8</font></i></a></i>;<br/>
<a NAME="E5:23"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="functor3.html#E1:23"><i><font color="Green">E7</font></i></a></i>;<br/>
<a NAME="E6:23"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="functor0.html#D19">FUNCTOR0:def 19</a></i>;<br/>
<b>hence </b><a NAME="E7:23"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor3.html#K1" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="functor3.html#E3:23"><i><font color="Green">E9</font></i></a>, <a class="txt" href="functor3.html#E4:23"><i><font color="Green">E10</font></i></a>, <a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/>


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