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<span class="kw">thus </span><a NAME="E1:95_1_1"/>
( <font color="Maroon" title="c1">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  implies  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">T</font> holds   <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Olive" title="b1">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</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"> ( (  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">T</font> holds   <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Olive" title="b1">a</font> ) implies <font color="Maroon" title="c1">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:95_1_1"/><span class="lab"><font color="Green" title="E52">A1</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">T</font> holds   <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Olive" title="b1">a</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"> <font color="Maroon" title="c1">T</font> is  <a href="abcmiz_0.html#V12" title="ABCMIZ_0:attr.12">non-absorbing</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="95_1_1_1"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</font> holds  <span class="p1">(<span class="default"> the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T</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"> <span class="p1">(<span class="default"> the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">x</font> as   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font> ;<br/><span class="kw">thus </span><span class="p1">(<span class="default"> the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> = 
 <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" title="ABCMIZ_0:func.1">non-</a> <font color="Maroon" title="c3">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<br/>.= 
 <a href="abcmiz_0.html#K10" title="ABCMIZ_0:func.10">sub</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95_1_1"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>
<br/>.= 
 the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:95_1_1"/>
 the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a>  the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  the <a href="abcmiz_0.html#U4" title="ABCMIZ_0:sel.4">sub-map</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="abcmiz_0.html#D24" target="_self" onmouseover="rs('abcmiz_0/D24')" onmouseout="rh()">ABCMIZ_0:def 24</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"> verum</span><br/>


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