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<b>let </b><font color="Maroon" title="c1">N</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">seq1</font>, <font color="Maroon" title="c3">seq2</font>, <font color="Maroon" title="c4">seq3</font> be   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Maroon" title="c1">N</font>;<br/>







<b>thus </b><font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K4" title="TOPRNS_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">seq2</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <font color="Maroon" title="c4">seq3</font></span>)</span> = 
<font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" title="TOPRNS_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">seq2</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <font color="Maroon" title="c4">seq3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="toprns_1.html#T12" target="_self" title="TOPRNS_1:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" title="TOPRNS_1:func.2">*</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" title="TOPRNS_1:func.2">*</a> <font color="Maroon" title="c4">seq3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="toprns_1.html#T13" target="_self" title="TOPRNS_1:th.13">Th13</a></i>
<br/>.= 
<font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" title="TOPRNS_1:func.2">*</a> <font color="Maroon" title="c4">seq3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="toprns_1.html#T12" target="_self" title="TOPRNS_1:th.12">Th12</a></i>
<br/>.= 
<font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <span class="p2">(<span class="default"><a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c4">seq3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="toprns_1.html#T12" target="_self" title="TOPRNS_1:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="toprns_1.html#K4" title="TOPRNS_1:func.4">-</a> <font color="Maroon" title="c3">seq2</font></span>)</span> <a href="toprns_1.html#K4" title="TOPRNS_1:func.4">-</a> <font color="Maroon" title="c4">seq3</font>
<b>by </b><i><a class="ref" href="toprns_1.html#T11" target="_self" title="TOPRNS_1:th.11">Th11</a></i>
;<br/>


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