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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>; <a class="txt" 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 <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span><br/>  for <font color="Olive" title="b2">x1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x1</font> holds <br/><font color="Olive" title="b1">x</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x1</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font>  st <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> holds <br/><font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">hp</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">hp</font> implies <font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:49"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">hp</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">hpd</font> = <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> ;<br/>
<a NAME="E2:49"/>
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span>
 
;<br/>
<a NAME="E3:49"/><span class="kw">then </span>
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="uniroots.html#D1" title="UNIROOTS:def.1">UNIROOTS:def 1</a></span>;<br/>
<a NAME="E4:49"/><span class="kw">then </span>
 not <font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E5:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c2">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:49"/><span class="kw">then </span>
<font color="Maroon" title="c3">hp</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>;<br/>
<a NAME="E7:49"/><span class="kw">then </span>
<font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T6" title="VECTSP_1:th.6">VECTSP_1:6</a></span>;<br/>
<a NAME="E8:49"/><span class="kw">then </span>
 not <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:49"/><span class="kw">then </span>
<font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">g</font> = <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="uniroots.html#D1" title="UNIROOTS:def.1">UNIROOTS:def 1</a></span>;<br/>
<a NAME="E11:49"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="uniroots.html#T17" title="UNIROOTS:th.17">UNIROOTS:17</a></span>;<br/>
<font color="Maroon" title="c5">g</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">hp</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="uniroots.html#T16" title="UNIROOTS:th.16">UNIROOTS:16</a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E5:49"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E11:49"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:49"/>
<font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">hp</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></span>; <a class="txt" 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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