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<span class="kw">let </span><font color="Maroon" title="c1">a1</font>, <font color="Maroon" title="c2">n1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">n2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">x</font> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font> holds <br/> for <font color="Olive" title="b2">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds  <font color="Olive" title="b1">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">x</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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="c5">x</font> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font> implies  for <font color="Olive" title="b1">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds  <font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:25"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</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">  for <font color="Olive" title="b1">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds  <font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="number14.html#R1" title="NUMBER14:pred.1">solves_CRT</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">n1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">n2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>;<br/>
<a NAME="E2:25"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c2">n1</font>
 
;<br/>
<a NAME="E3:25"/><span class="kw">then </span>
<font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>,<font color="Maroon" title="c1">a1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c2">n1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="int_1.html#T16" onmouseover="rs('int_1/T16')" onmouseout="rh()">INT_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:25"/>
<font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>,<font color="Maroon" title="c1">a1</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c2">n1</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="number14.html#D1" target="_self" onmouseover="rs('number14/D1')" onmouseout="rh()">NUMBER14:def 1</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="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>,<font color="Maroon" title="c3">a2</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c4">n2</font></span><br/>

<a NAME="E5:25"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c4">n2</font>
 
;<br/>
<a NAME="E6:25"/><span class="kw">then </span>
<font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>,<font color="Maroon" title="c3">a2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c4">n2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="int_1.html#T16" onmouseover="rs('int_1/T16')" onmouseout="rh()">INT_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:25"/>
<font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">n2</font></span>)</span>,<font color="Maroon" title="c3">a2</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Maroon" title="c4">n2</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"> verum</span><br/>


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