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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="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K2">"</a>  <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:49"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>and </b><br/><a NAME="E5:49"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:49"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K2">"</a>  <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D9" target="_self">CIRCTRM1:def 9</a><br/>

<b>thus </b><a NAME="E7:49"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 <b>by </b><i><a class="txt" href="circtrm1.html#E1:49"><i><font color="Green">E32</font></i></a>, <a class="txt" href="circtrm1.html#E4:49"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T46">FUNCT_1:46</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D9" target="_self">CIRCTRM1:def 9</a><br/>

<a NAME="E8:49"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="circtrm1.html#E1:49"><i><font color="Green">E32</font></i></a>, <a class="txt" href="circtrm1.html#E4:49"><i><font color="Green">E35</font></i></a>, <a class="ref" href="funct_1.html#T66">FUNCT_1:66</a></i>;<br/>
<b>hence </b><a NAME="E9:49"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K2">"</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K2">"</a>  <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="circtrm1.html#E2:49"><i><font color="Green">E33</font></i></a>, <a class="txt" href="circtrm1.html#E3:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="circtrm1.html#E5:49"><i><font color="Green">E36</font></i></a>, <a class="txt" href="circtrm1.html#E6:49"><i><font color="Green">E37</font></i></a>, <a class="ref" href="pua2mss1.html#T30">PUA2MSS1:30</a></i>;<br/>


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