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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <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="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies <font color="Maroon" title="c1">S</font> is  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:5_1_1"/><span class="lab"><font color="Green" title="E2">Z</font></span>: 
<font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <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="c1">S</font> is  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:5_1_1"/>
 not <font color="Maroon" title="c1">S</font> is  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring1.html#D2" target="_self" title="SCMRING1:def.2">Def2</a></span>;<br/>
<a NAME="E4:5_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5_1_1"><span class="lab"><font color="Green" title="E2">Z</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:5_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:5_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></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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