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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font>;<br/>









<a NAME="E1:127"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font>, B is    <a href="finseq_2.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font> : verum </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E2:127"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>5</sub></font> is    <a href="finseq_2.html#M2" target="_self">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_2.html#K4" target="_self">-tuples_on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T125" target="_self">Th125</a></i>;<br/>


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