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<span class="kw">let </span><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font>, <font color="Maroon" title="c3">K</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">B</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c2">J</font><br/> for <font color="Olive" title="b3">C</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c3">K</font>  st <font color="Olive" title="b1">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b2">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b3">C</font> holds <br/><font color="Olive" title="b1">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b3">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c2">J</font><br/> for <font color="Olive" title="b2">C</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c3">K</font>  st <font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b1">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b2">C</font> holds <br/><font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b2">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">B</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c2">J</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">C</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c3">K</font>  st <font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c5">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b1">C</font> holds <br/><font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Olive" title="b1">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">C</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c3">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c5">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c6">C</font> implies <font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c6">C</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c6">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c6">C</font></span><br/>

<a NAME="E3:17"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">J</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></span>;<br/>
<a NAME="E4:17"/>
<font color="Maroon" title="c2">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:17"/>
<font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">ALTCAT_2:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E6:17"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span><br/>

<a NAME="E7:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></span>;<br/>
<a NAME="E8:17"/>
<font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:17"/>
<font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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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