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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be    <a href="struct_0.html#L4" title="STRUCT_0:struct.4">ZeroOneStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  implies  not <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
not <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/>

<span class="kw">assume </span><a NAME="E2:31_1_1"/>
<font color="Maroon" title="c1">L</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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:31_1_1"/><span class="kw">then </span>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</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="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" target="_self" title="STRUCT_0:def.10">Def10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:31_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="struct_0.html#D8" target="_self" title="STRUCT_0:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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