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<span class="kw">reconsider </span><font color="Maroon" title="c3">c</font> =  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c5">A2</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_1.html#V6" title="ALTCAT_1:attr.6">strict</a>   <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> &amp; ( for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> holds  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> ) &amp; ( for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">A1</font><br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> holds <br/><span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c4">A1</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</font> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <font color="Olive" title="b4">f</font> ) &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> &amp; ( for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> holds  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> ) &amp; ( for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">A2</font><br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> holds <br/><span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c5">A2</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</font> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <font color="Olive" title="b4">f</font> ) implies <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">A2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:12_1_2"/><span class="lab"><font color="Green" title="E8">A25</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E3:12_1_2"/><span class="lab"><font color="Green" title="E9">A26</font></span>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> holds  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 <span class="kw">and </span><br/><a NAME="E4:12_1_2"/><span class="lab"><font color="Green" title="E10">A27</font></span>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">A1</font><br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> holds <br/><span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c4">A1</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</font> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <font color="Olive" title="b4">f</font>
 <span class="kw">and </span><br/><a NAME="E5:12_1_2"/><span class="lab"><font color="Green" title="E11">A28</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E6:12_1_2"/><span class="lab"><font color="Green" title="E12">A29</font></span>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msinst_1.html#K2" title="MSINST_1:func.2">MSAlg_set</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font> holds  the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 <span class="kw">and </span><br/><a NAME="E7:12_1_2"/><span class="lab"><font color="Green" title="E13">A30</font></span>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">k</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">A2</font><br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font> holds <br/><span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c5">A2</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b3">k</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</font> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <font color="Olive" title="b4">f</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">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">A2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">CC1</font> = the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c7">CC2</font> = the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c5">A2</font> as   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E8">A25</font></span></a>, <a class="txt" href="#E5:12_1_2"><span class="lab"><font color="Green" title="E11">A28</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">AA1</font> = the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c4">A1</font>, <font color="Maroon" title="c9">AA2</font> = the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c5">A2</font> as   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E8">A25</font></span></a>, <a class="txt" href="#E5:12_1_2"><span class="lab"><font color="Green" title="E11">A28</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E14">A31</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c11">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">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="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> = 
 <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_2"><span class="lab"><font color="Green" title="E9">A26</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1_2"><span class="lab"><font color="Green" title="E12">A29</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E11:12_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A32</font></span>: 
<font color="Maroon" title="c8">AA1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c9">AA2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_1.html#T9" title="ALTCAT_1:th.9">ALTCAT_1:9</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c11">j</font>, <font color="Maroon" title="c12">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"> ( <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c12">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font> implies <font color="Maroon" title="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> )</span><br/><span class="kw">set </span><font color="Maroon" title="c13">ijk</font> = <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>;<br/><a NAME="E1:12_1_2_2"/><span class="lab"><font color="Green" title="E16">A33</font></span>: 
<font color="Maroon" title="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">CC1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:12_1_2_2"/><span class="lab"><font color="Green" title="E17">A34</font></span>: 
( <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c12">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">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="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">i9</font> = <font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c15">j9</font> = <font color="Maroon" title="c11">j</font>, <font color="Maroon" title="c16">k9</font> = <font color="Maroon" title="c12">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">c</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">I9</font> = <font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c18">J9</font> = <font color="Maroon" title="c11">j</font>, <font color="Maroon" title="c19">K9</font> = <font color="Maroon" title="c12">k</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c5">A2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1_2"><span class="lab"><font color="Green" title="E11">A28</font></span></a>, <a class="txt" href="#E2:12_1_2_2"><span class="lab"><font color="Green" title="E17">A34</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c20">I</font> = <font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c21">J</font> = <font color="Maroon" title="c11">j</font>, <font color="Maroon" title="c22">K</font> = <font color="Maroon" title="c12">k</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c4">A1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E8">A25</font></span></a>, <a class="txt" href="#E2:12_1_2_2"><span class="lab"><font color="Green" title="E17">A34</font></span></a></span>;<br/><a NAME="E6:12_1_2_2"/><span class="lab"><font color="Green" title="E18">A35</font></span>: 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2_2"><span class="lab"><font color="Green" title="E17">A34</font></span></a>, <a class="ref" href="mcart_1.html#T73" title="MCART_1:th.73">MCART_1:73</a></span>;<br/><a NAME="E7:12_1_2_2"/><span class="lab"><font color="Green" title="E19">A36</font></span>: 
<font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/><span class="kw">thus </span><a NAME="E8:12_1_2_2"/>
<font color="Maroon" title="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c23">Cj</font> = <font color="Maroon" title="c7">CC2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c9">AA2</font>,<font color="Maroon" title="c9">AA2</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c9">AA2</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1_2"><span class="lab"><font color="Green" title="E11">A28</font></span></a>, <a class="txt" href="#E6:12_1_2_2"><span class="lab"><font color="Green" title="E18">A35</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">Ci</font> = <font color="Maroon" title="c6">CC1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E8">A25</font></span></a>, <a class="txt" href="#E6:12_1_2_2"><span class="lab"><font color="Green" title="E18">A35</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_2_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:12_1_2_2_1_1"/>
( <span class="p1"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <span class="p1"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_2_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:12_1_2_2_1_1_1"/><span class="lab"><font color="Green" title="E20">A37</font></span>: 
<span class="p1"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><br/><div class="add"><a NAME="E2:12_1_2_2_1_1_1"/><span class="lab"><font color="Green" title="E21">A38</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> holds <br/><font color="Maroon" title="c24">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Cj</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_2_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">x</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="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> implies <font color="Maroon" title="c24">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Cj</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:12_1_2_2_1_1_1_1"/><span class="lab"><font color="Green" title="E22">A39</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <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="c24">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Cj</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font></span><br/>

<a NAME="E2:12_1_2_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/>
<a NAME="E3:12_1_2_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A40</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2_2"><span class="lab"><font color="Green" title="E17">A34</font></span></a>, <a class="ref" href="altcat_1.html#D6" title="ALTCAT_1:def.6">ALTCAT_1:def 6</a></span>;<br/>
<a NAME="E4:12_1_2_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A41</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></span>;<br/>
<a NAME="E5:12_1_2_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c15">j9</font>,<font color="Maroon" title="c16">k9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_2"><span class="lab"><font color="Green" title="E9">A26</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">M2</font>, <font color="Maroon" title="c27">N2</font> being   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c28">g</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c26">M2</font>,<font color="Maroon" title="c27">N2</font><span class="kw"> such that </span><br/><a NAME="E7:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c26">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">j9</font>
 <span class="kw">and </span><br/><a NAME="E8:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c27">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">k9</font>
 <span class="kw">and </span><br/><a NAME="E9:12_1_2_2_1_1_1_1"/><span class="lab"><font color="Green" title="E25">A42</font></span>: 
<font color="Maroon" title="c28">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
 <span class="kw">and </span><br/><a NAME="E10:12_1_2_2_1_1_1_1"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c26">M2</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c27">N2</font>
 <span class="kw">and </span><br/><a NAME="E11:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c28">g</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c26">M2</font>,<font color="Maroon" title="c27">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msinst_1.html#D3" target="_self" title="MSINST_1:def.3">Def3</a></span>;<br/>
<a NAME="E12:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c9">AA2</font>,<font color="Maroon" title="c9">AA2</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:12_1_2"><span class="lab"><font color="Green" title="E15">A32</font></span></a>, <a class="txt" href="#E1:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E22">A39</font></span></a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>;<br/>
<a NAME="E13:12_1_2_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2_2"><span class="lab"><font color="Green" title="E17">A34</font></span></a>, <a class="ref" href="altcat_1.html#D6" title="ALTCAT_1:def.6">ALTCAT_1:def 6</a></span>;<br/>
<a NAME="E14:12_1_2_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A43</font></span>: 
( <font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> &amp; <font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">AA2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></span>;<br/>
<a NAME="E15:12_1_2_2_1_1_1_1"/><span class="lab"><font color="Green" title="E27">A44</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">AA1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E23">A40</font></span></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></span>;<br/>
<a NAME="E16:12_1_2_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msinst_1.html#K3" title="MSINST_1:func.3">MSAlg_morph</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c14">i9</font>,<font color="Maroon" title="c15">j9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_2"><span class="lab"><font color="Green" title="E9">A26</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">M1</font>, <font color="Maroon" title="c30">N1</font> being   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c31">f</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c29">M1</font>,<font color="Maroon" title="c30">N1</font><span class="kw"> such that </span><br/><a NAME="E18:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c29">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i9</font>
 <span class="kw">and </span><br/><a NAME="E19:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c30">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">j9</font>
 <span class="kw">and </span><br/><a NAME="E20:12_1_2_2_1_1_1_1"/><span class="lab"><font color="Green" title="E28">A45</font></span>: 
<font color="Maroon" title="c31">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">and </span><br/><a NAME="E21:12_1_2_2_1_1_1_1"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c29">M1</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c30">N1</font>
 <span class="kw">and </span><br/><a NAME="E22:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c31">f</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c29">M1</font>,<font color="Maroon" title="c30">N1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msinst_1.html#D3" target="_self" title="MSINST_1:def.3">Def3</a></span>;<br/>
<a NAME="E23:12_1_2_2_1_1_1_1"/><span class="lab"><font color="Green" title="E29">A46</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c28">g</font>,<font color="Maroon" title="c31">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E23">A40</font></span></a>, <a class="txt" href="#E20:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E9:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E25">A42</font></span></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c24">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> = 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c4">A1</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c20">I</font>,<font color="Maroon" title="c21">J</font>,<font color="Maroon" title="c22">K</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c28">g</font>,<font color="Maroon" title="c31">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c28">g</font> <a href="pboole.html#K10" title="PBOOLE:func.10">**</a> <font color="Maroon" title="c31">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1_2"><span class="lab"><font color="Green" title="E10">A27</font></span></a>, <a class="txt" href="#E4:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E24">A41</font></span></a>, <a class="txt" href="#E15:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E27">A44</font></span></a>, <a class="txt" href="#E20:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E9:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E25">A42</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon" title="c5">A2</font> <a href="altcat_1.html#K4" title="ALTCAT_1:func.4">.</a> <font color="Maroon" title="c17">I9</font>,<font color="Maroon" title="c18">J9</font>,<font color="Maroon" title="c19">K9</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c28">g</font>,<font color="Maroon" title="c31">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:12_1_2"><span class="lab"><font color="Green" title="E13">A30</font></span></a>, <a class="txt" href="#E14:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E26">A43</font></span></a>, <a class="txt" href="#E20:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E9:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E25">A42</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c23">Cj</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:12_1_2_2_1_1_1_1"><span class="lab"><font color="Green" title="E29">A46</font></span></a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E25:12_1_2_2_1_1_1_1"/>
<font color="Maroon" title="c24">Ci</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Cj</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:12_1_2_2_1_1_1"/>
<span class="p1"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c9">AA2</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1_2"><span class="lab"><font color="Green" title="E14">A31</font></span></a>, <a class="txt" href="#E1:12_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E20">A37</font></span></a>, <a class="ref" href="altcat_1.html#T9" title="ALTCAT_1:th.9">ALTCAT_1:9</a></span>;<br/><a NAME="E4:12_1_2_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A47</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c23">Cj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c9">AA2</font>,<font color="Maroon" title="c9">AA2</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E5:12_1_2_2_1_1_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c24">Ci</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font>,<font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K3" title="ALTCAT_1:func.3">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E20">A37</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:12_1_2_2_1_1_1"/>
<font color="Maroon" title="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:12_1_2"><span class="lab"><font color="Green" title="E15">A32</font></span></a>, <a class="txt" href="#E1:12_1_2_2"><span class="lab"><font color="Green" title="E16">A33</font></span></a>, <a class="txt" href="#E7:12_1_2_2"><span class="lab"><font color="Green" title="E19">A36</font></span></a>, <a class="txt" href="#E4:12_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E22">A47</font></span></a>, <a class="txt" href="#E2:12_1_2_2_1_1_1"><span class="lab"><font color="Green" title="E21">A38</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_2_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:12_1_2_2_1_1_2"/>
<span class="p1"><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">{|</a><span class="default"><font color="Maroon" title="c8">AA1</font></span><a href="altcat_1.html#K2" title="ALTCAT_1:func.2">|}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font></span><br/><div class="add"><a NAME="E2:12_1_2_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c24">Ci</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c23">Cj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:12_1_2"><span class="lab"><font color="Green" title="E15">A32</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:12_1_2_2_1_1_2"/>
<font color="Maroon" title="c6">CC1</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">CC2</font> <a href="multop_1.html#K1" title="MULTOP_1:func.1">.</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>,<font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_2_2"><span class="lab"><font color="Green" title="E16">A33</font></span></a>, <a class="ref" href="multop_1.html#D1" title="MULTOP_1:def.1">MULTOP_1:def 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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:12_1_2"/>
<font color="Maroon" title="c4">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">A2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E8">A25</font></span></a>, <a class="txt" href="#E5:12_1_2"><span class="lab"><font color="Green" title="E11">A28</font></span></a>, <a class="txt" href="#E11:12_1_2"><span class="lab"><font color="Green" title="E15">A32</font></span></a>, <a class="ref" href="altcat_1.html#T10" title="ALTCAT_1:th.10">ALTCAT_1:10</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/>


</div>
