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<span class="kw">let </span><font color="Maroon" title="c1">I</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">A</font>, <font color="Olive" title="b2">M</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="b3">B</font>, <font color="Olive" title="b4">C</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <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="b5">F</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive" title="b1">A</font>,<span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Olive" title="b3">B</font>,<font color="Olive" title="b4">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>  st <font color="Olive" title="b2">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Olive" title="b5">F</font> holds <br/> for <font color="Olive" title="b6">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Olive" title="b5">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Olive" title="b5">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Olive" title="b2">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">M</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">  for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">C</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <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="b3">F</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>  st <font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Olive" title="b3">F</font> holds <br/> for <font color="Olive" title="b4">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">  for <font color="Olive" title="b1">F</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>  st <font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Olive" title="b1">F</font> holds <br/> for <font color="Olive" title="b2">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">F</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</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"> ( <font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Maroon" title="c6">F</font> implies  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>











<span class="kw">assume </span><a NAME="E1:31"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Maroon" title="c6">F</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">  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">i</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"> ( <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:31"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">I</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"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<a NAME="E3:31"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_6.html#K1" title="FUNCT_6:func.1">doms</a> <font color="Maroon" title="c6">F</font></span>)</span> <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="#E1:31"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>;<br/>
<a NAME="E4:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="mssubfam.html#T14" onmouseover="rs('mssubfam/T14')" onmouseout="rh()">MSSUBFAM:14</a></span>;<br/>
<a NAME="E5:31"/>
<font color="Maroon" title="c2">A</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> <span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>
 
;<br/>
<a NAME="E6:31"/><span class="kw">then </span>
<font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="mssubfam.html#T17" onmouseover="rs('mssubfam/T17')" onmouseout="rh()">MSSUBFAM:17</a></span>;<br/>
<a NAME="E7:31"/><span class="kw">then </span>
<font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="closure1.html#T3" onmouseover="rs('closure1/T3')" onmouseout="rh()">CLOSURE1:3</a></span>;<br/>
<a NAME="E8:31"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span> <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="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a></span>;<br/>
<a NAME="E9:31"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="tarski.html#R2" title="TARSKI: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="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="pboole.html#D16" onmouseover="rs('pboole/D16')" onmouseout="rh()">PBOOLE:def 16</a></span>;<br/>
<a NAME="E10:31"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="tarski.html#R2" title="TARSKI: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="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="pralg_1.html#D20" onmouseover="rs('pralg_1/D20')" onmouseout="rh()">PRALG_1:def 20</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">z</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>;<br/>
<a NAME="E11:31"/>
<span class="p1">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mcart_1.html#K12" title="MCART_1:func.12">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="msualg_9.html#D2" target="_self" onmouseover="rs('msualg_9/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E16">A5</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> = 
<span class="p1">(<span class="default"><a href="mcart_1.html#K12" title="MCART_1:func.12">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="pralg_1.html#D20" onmouseover="rs('pralg_1/D20')" onmouseout="rh()">PRALG_1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="mcart_1.html#D13" onmouseover="rs('mcart_1/D13')" onmouseout="rh()">MCART_1:def 13</a></span>
;<br/>
<a NAME="E13:31"/>
<span class="p1">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mcart_1.html#K11" title="MCART_1:func.11">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="msualg_9.html#D1" target="_self" onmouseover="rs('msualg_9/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> = 
<span class="p1">(<span class="default"><a href="mcart_1.html#K11" title="MCART_1:func.11">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="pralg_1.html#D20" onmouseover="rs('pralg_1/D20')" onmouseout="rh()">PRALG_1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:31"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="mcart_1.html#D12" onmouseover="rs('mcart_1/D12')" onmouseout="rh()">MCART_1:def 12</a></span>
;<br/>
<a NAME="E15:31"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:31"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E12:31"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="mcart_1.html#T21" onmouseover="rs('mcart_1/T21')" onmouseout="rh()">MCART_1:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:31"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K1" title="MSUALG_9:func.1">Mpr1</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msualg_9.html#K2" title="MSUALG_9:func.2">Mpr2</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="pralg_1.html#K18" title="PRALG_1:func.18">..</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="pralg_1.html#D20" onmouseover="rs('pralg_1/D20')" onmouseout="rh()">PRALG_1:def 20</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/>


</div>
