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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:6_1_1"/>
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>then reconsider </b><font color="Maroon" title="c2">T</font> = <font color="Maroon" title="c1">S</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  ;<br/>
<b>assume </b><a NAME="E3:6_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:6_1_1"/><b>then </b><i><font color="Green" title="E2">A1</font></i>: 
( 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="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  or 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="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="scmring1.html#D2" target="_self" title="SCMRING1:def.2">Def2</a></i>;<br/>
<a NAME="E5:6_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 
;<br/>
<b>hence </b><a NAME="E6:6_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring1.html#E4:6_1_1"><i><font color="Green" title="E2">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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