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<b>let </b><font color="Maroon" title="c1">n</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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">z1</font>, <font color="Maroon" title="c3">z2</font> be   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c1">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E1:26"/>
<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font> <a href="binarith.html#R1" title="BINARITH:pred.1">are_summable</a> 
 ;<br/>

<a NAME="E2:26"/><b>then </b>
 <a href="binarith.html#K9" title="BINARITH:func.9">add_ovfl</a> <font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 
<b>by </b><i><a class="ref" href="binarith.html#D10" target="_self" title="BINARITH:def.10">Def10</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
 <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">IFEQ</a> <span class="p1">(<span class="default"><a href="binarith.html#K9" title="BINARITH:func.9">add_ovfl</a> <font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font></span>)</span>,<a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>;<br/>
<b>hence </b> <a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K8" title="BINARITH:func.8">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K8" title="BINARITH:func.8">+</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K13" title="FUNCOP_1:func.13">IFEQ</a> <span class="p2">(<span class="default"><a href="binarith.html#K9" title="BINARITH:func.9">add_ovfl</a> <font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font></span>)</span>,<a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><a href="binarith.html#K7" title="BINARITH:func.7">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T47" target="_self" title="BINARITH:th.47">Th47</a></i>
;<br/><br/>


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