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<span class="kw">let </span><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font> being    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b1">D1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Olive" title="b2">D2</font> holds <br/><font color="Olive" title="b1">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">D2</font> is    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">D1</font>, <font color="Maroon" title="c4">D2</font> be    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">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="c3">D1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">D2</font> implies <font color="Maroon" title="c3">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">D2</font> is    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">D</font> = <font color="Maroon" title="c3">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">D2</font>;<br/>
<span class="kw">assume </span><a NAME="E1:48"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c3">D1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">D2</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="c3">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">D2</font> is    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E2:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c3">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">D2</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T51" onmouseover="rs('partfun1/T51')" onmouseout="rh()">PARTFUN1:51</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">S1</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E4:48"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c6">S1</font> <a href="nomin_1.html#R2" title="NOMIN_1:pred.2">IsNDRankSeq</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E5:48"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<font color="Maroon" title="c3">D1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c6">S1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D5" target="_self" onmouseover="rs('nomin_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">S2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E7:48"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
<font color="Maroon" title="c7">S2</font> <a href="nomin_1.html#R2" title="NOMIN_1:pred.2">IsNDRankSeq</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E8:48"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
<font color="Maroon" title="c4">D2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Maroon" title="c7">S2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D5" target="_self" onmouseover="rs('nomin_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E9:48"/>
( <font color="Maroon" title="c6">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">S2</font> or <font color="Maroon" title="c7">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">S1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E7:48"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="nomin_1.html#T22" target="_self" onmouseover="rs('nomin_1/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:48"/>
<font color="Maroon" title="c3">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">D2</font> is    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="txt" href="#E7:48"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E8:48"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="nomin_1.html#T35" target="_self" onmouseover="rs('nomin_1/T35')" onmouseout="rh()">Th35</a>, <a class="ref" href="nomin_1.html#D5" target="_self" onmouseover="rs('nomin_1/D5')" onmouseout="rh()">Def5</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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