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<span class="kw">thus </span><a NAME="E1:37"/>
for <font color="Olive" title="b1">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>  holds  <a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">z</font>,<font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="binop_1.html#D7" title="BINOP_1:def.7">BINOP_1:def 7</a>,<a class="ref" href="binop_1.html#D16" title="BINOP_1:def.16">BINOP_1:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">z</font> <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a>  <a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font></span><br/>

<span class="kw">thus </span><a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <font color="Maroon" title="c3">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D15" target="_self" title="BINOP_2:def.15">Def15</a></span>
<br/>.= 
<font color="Maroon" title="c3">w</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="binop_1.html#D17" title="BINOP_1:def.17">BINOP_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font></span><br/>

<span class="kw">thus </span><a href="binop_2.html#K39" title="BINOP_2:func.39">addrat</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">z</font> = 
<font color="Maroon" title="c3">w</font> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D15" target="_self" title="BINOP_2:def.15">Def15</a></span>
<br/>.= 
<font color="Maroon" title="c3">w</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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