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<span class="kw">let </span><font color="Maroon" title="c3">K1</font> be    <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</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">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a></span><br/>

<span class="kw">thus </span><a NAME="E1:73"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c4">x</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 <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> or <font color="Maroon" title="c4">x</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 <font color="Maroon" title="c3">K1</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">C1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font>;<br/>
<a NAME="E2:73"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T24" target="_self" onmouseover="rs('gaussint/T24')" onmouseout="rh()">Th24</a></span>;<br/>
<a NAME="E3:73"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
 <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T23" target="_self" onmouseover="rs('gaussint/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:73"/>
<font color="Maroon" title="c4">x</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 <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</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"> <font color="Maroon" title="c4">x</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 <font color="Maroon" title="c3">K1</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">x1</font> = <font color="Maroon" title="c4">x</font> as   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">m</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>, <font color="Maroon" title="c8">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E7:73"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
( <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c8">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#T8" onmouseover="rs('rat_1/T8')" onmouseout="rh()">RAT_1:8</a></span>;<br/>
<a NAME="E8:73"/><span class="lab"><font color="Green" title="E33">A4</font></span>: 
<font color="Maroon" title="c7">m</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 <font color="Maroon" title="c3">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="int_1.html#D2" onmouseover="rs('int_1/D2')" onmouseout="rh()">INT_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">k2</font> = <font color="Maroon" title="c8">k</font>, <font color="Maroon" title="c10">m2</font> = <font color="Maroon" title="c7">m</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#D2" onmouseover="rs('rat_1/D2')" onmouseout="rh()">RAT_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">k0</font> = <font color="Maroon" title="c8">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/>
<a NAME="E11:73"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<font color="Maroon" title="c11">k0</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> <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E32">A3</font></span></a></span>;<br/>
<a NAME="E12:73"/><span class="kw">then </span>
<font color="Maroon" title="c11">k0</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="c3">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">k0i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K1</font><span class="kw"> such that </span><br/><a NAME="E14:73"/><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<font color="Maroon" title="c12">k0i</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c11">k0</font> <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="c3">K1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D9" onmouseover="rs('vectsp_1/D9')" onmouseout="rh()">VECTSP_1:def 9</a></span>;<br/>
<a NAME="E15:73"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">kk0</font> = <font color="Maroon" title="c12">k0i</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> ;<br/>
<font color="Maroon" title="c13">kk0</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">k2</font> = 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">K1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:73"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="gaussint.html#T18" target="_self" onmouseover="rs('gaussint/T18')" onmouseout="rh()">Th18</a></span>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>
;<br/>
<a NAME="E18:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A7</font></span>: 
<font color="Maroon" title="c13">kk0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k2</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="vectsp_1.html#D10" onmouseover="rs('vectsp_1/D10')" onmouseout="rh()">VECTSP_1:def 10</a></span>;<br/>
<a NAME="E19:73"/><span class="lab"><font color="Green" title="E37">A8</font></span>: 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">K1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D1" onmouseover="rs('ec_pf_1/D1')" onmouseout="rh()">EC_PF_1:def 1</a></span>;<br/>
<font color="Maroon" title="c7">m</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c8">k</font> = 
<font color="Maroon" title="c10">m2</font> <a href="quofield.html#K20" title="QUOFIELD:func.20">/</a> <font color="Maroon" title="c9">k2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T16" target="_self" onmouseover="rs('gaussint/T16')" onmouseout="rh()">Th16</a>, <a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E32">A3</font></span></a></span>
<br/>.= 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">K1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c10">m2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">k2</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:73"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="txt" href="#E18:73"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="txt" href="#E19:73"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E21:73"/>
<font color="Maroon" title="c4">x</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 <font color="Maroon" title="c3">K1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="txt" href="#E8:73"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="txt" href="#E18:73"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="ref" href="binop_1.html#T17" onmouseover="rs('binop_1/T17')" onmouseout="rh()">BINOP_1:17</a></span>; <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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