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<span class="kw">let </span><font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c2">A2</font> be    <a href="abcmiz_0.html#L1" title="ABCMIZ_0:struct.1">AdjectiveStr</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"> (  <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">A1</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c2">A2</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">A2</font> #) &amp; <font color="Maroon" title="c1">A1</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  implies <font color="Maroon" title="c2">A2</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:18"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">A1</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#G1" title="ABCMIZ_0:aggr.1">AdjectiveStr</a>(#  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c2">A2</font>, the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">A2</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"> (  not <font color="Maroon" title="c1">A1</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  or <font color="Maroon" title="c2">A2</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:18"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 for <font color="Olive" title="b1">a</font> being   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">A1</font>  holds  not  <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D7" target="_self" onmouseover="rs('abcmiz_0/D7')" onmouseout="rh()">ABCMIZ_0:def 7</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="c2">A2</font> is  <a href="abcmiz_0.html#V6" title="ABCMIZ_0:attr.6">without_fixpoints</a> </span><br/>

<span class="kw">given </span><font color="Maroon" title="c3">a</font> being   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c2">A2</font><span class="kw"> such that </span><a NAME="E4:18"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
 <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D7" target="_self" onmouseover="rs('abcmiz_0/D7')" onmouseout="rh()">ABCMIZ_0:def 7</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"> contradiction</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">b</font> = <font color="Maroon" title="c3">a</font> as   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">A1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E9">A1</font></span></a></span>;<br/>
<a NAME="E6:18"/>
 <a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E11">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:18"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E10">A2</font></span></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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