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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1a.html#V1" title="GROUP_1A:attr.1">add-unital</a>   <a href="algstr_0.html#L1" title="ALGSTR_0:struct.1">addMagma</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="group_1a.html#K4" title="GROUP_1A:func.4">mult</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (2,<font color="Olive" title="b1">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="group_1a.html#K4" title="GROUP_1A:func.4">mult</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (2,<font color="Maroon" title="c2">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font></span><br/>



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1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="group_1a.html#K4" title="GROUP_1A:func.4">mult</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (2,<font color="Maroon" title="c2">x</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1a.html#K4" title="GROUP_1A:func.4">mult</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nat_1.html#K10" title="NAT_1:func.10">.</a> (1,<font color="Maroon" title="c2">x</font>)</span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1a.html#D6" target="_self" onmouseover="rs('group_1a/D6')" onmouseout="rh()">Def7</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1a.html#T45" target="_self" onmouseover="rs('group_1a/T45')" onmouseout="rh()">Th49</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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