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<span class="kw">let </span><font color="Maroon" title="c1">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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <span class="p1">(<span class="default"><a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">M</font> =  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">d</font> =  <a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">c</font> =  <a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">p</font> =  <a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">i</font> =  <a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:79_1"/>
 for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> iff <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> )
  <a class="txt" 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>, <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> holds <br/>( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> ) ) &amp; (  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<font color="Olive" title="b2">g</font>)</span>)</span>,<font color="Olive" title="b1">f</font>) ) &amp; (  for <font color="Olive" title="b1">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font> holds <br/> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; (  for <font color="Olive" title="b2">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> ) &amp; (  for <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> ) ) ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> iff <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> )</span><br/>

<a NAME="E1:79_1_1"/>
( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c8">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c7">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:79_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> iff <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E2:79_1"/>
 for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> holds <br/>( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> )
  <a class="txt" 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>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<font color="Olive" title="b2">g</font>)</span>)</span>,<font color="Olive" title="b1">f</font>) ) &amp; (  for <font color="Olive" title="b1">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font> holds <br/> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; (  for <font color="Olive" title="b2">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> ) &amp; (  for <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> ) ) ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> implies ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_1_2"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> )</span><br/>

<a NAME="E2:79_1_2"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c8">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c7">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<a NAME="E3:79_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_2"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>;<br/>
<a NAME="E4:79_1_2"/><span class="lab"><font color="Green" title="E53">A4</font></span>: 
( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c7">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c8">g</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<a NAME="E5:79_1_2"/>
(  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c7">f</font> &amp;  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c8">g</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_2"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E2:79_1_2"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="coh_sp.html#T44" target="_self" title="COH_SP:th.44">Th45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:79_1_2"/>
( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79_1_2"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="txt" href="#E4:79_1_2"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E3:79_1"/>
 for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">h</font>,<font color="Olive" title="b2">g</font>)</span>)</span>,<font color="Olive" title="b1">f</font>)
  <a class="txt" 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> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font> holds <br/> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; (  for <font color="Olive" title="b2">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> ) &amp; (  for <font color="Olive" title="b2">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font>, <font color="Maroon" title="c9">h</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> implies <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<font color="Maroon" title="c8">g</font>)</span>)</span>,<font color="Maroon" title="c7">f</font>) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:79_1_3"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font>
 <span class="kw">and </span><br/><a NAME="E2:79_1_3"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<font color="Maroon" title="c8">g</font>)</span>)</span>,<font color="Maroon" title="c7">f</font>)</span><br/>

<a NAME="E3:79_1_3"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
(  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">h</font> &amp;  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<a NAME="E4:79_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A8</font></span>: 
 <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c8">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_3"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="ref" href="coh_sp.html#T44" target="_self" title="COH_SP:th.44">Th45</a></span>;<br/>
<a NAME="E5:79_1_3"/><span class="lab"><font color="Green" title="E54">A9</font></span>: 
(  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> &amp;  <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<a NAME="E6:79_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A10</font></span>: 
 <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c9">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_3"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E2:79_1_3"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E3:79_1_3"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="coh_sp.html#T44" target="_self" title="COH_SP:th.44">Th45</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<font color="Maroon" title="c7">f</font>)</span>)</span>) = 
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">h</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</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="#E2:79_1_3"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E5:79_1_3"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>
<br/>.= 
<font color="Maroon" title="c9">h</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:79_1_3"><span class="lab"><font color="Green" title="E55">A10</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_3"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E2:79_1_3"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E3:79_1_3"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="txt" href="#E5:79_1_3"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="ref" href="coh_sp.html#T45" target="_self" title="COH_SP:th.45">Th46</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c8">g</font></span>)</span>,<font color="Maroon" title="c7">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="#E2:79_1_3"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E5:79_1_3"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="txt" href="#E4:79_1_3"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c9">h</font>,<font color="Maroon" title="c8">g</font>)</span>)</span>,<font color="Maroon" title="c7">f</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_3"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E3:79_1_3"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">let </span><font color="Maroon" title="c7">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> &amp; (  for <font color="Olive" title="b1">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> ) &amp; (  for <font color="Olive" title="b1">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> ) )</span><br/><a NAME="E4:79_1"/><span class="lab"><font color="Green" title="E50">A11</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K24" title="COH_SP:func.24">id$</a> <font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D28" target="_self" title="COH_SP:def.28">Def32</a></span>;<br/><a NAME="E5:79_1"/><span class="lab"><font color="Green" title="E51">A12</font></span>: 
 <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K24" title="COH_SP:func.24">id$</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T46" target="_self" title="COH_SP:th.46">Th47</a></span>;<br/><a NAME="E6:79_1"/><span class="lab"><font color="Green" title="E52">A13</font></span>: 
 <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K24" title="COH_SP:func.24">id$</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T46" target="_self" title="COH_SP:th.46">Th47</a></span>;<br/><span class="kw">hence </span><a NAME="E7:79_1"/>
( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> &amp; <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79_1"><span class="lab"><font color="Green" title="E50">A11</font></span></a>, <a class="txt" href="#E5:79_1"><span class="lab"><font color="Green" title="E51">A12</font></span></a>, <a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a>, <a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>; <a class="txt" 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="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> ) &amp; (  for <font color="Olive" title="b1">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> ) )</span><br/><span class="kw">thus </span><a NAME="E8:79_1"/>
 for <font color="Olive" title="b1">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>  st <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> holds <br/><span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">f</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> implies <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Maroon" title="c8">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_1_4"/><span class="lab"><font color="Green" title="E53">A14</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Maroon" title="c8">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font></span><br/>

<a NAME="E2:79_1_4"/><span class="lab"><font color="Green" title="E54">A15</font></span>: 
 <a href="coh_sp.html#K23" title="COH_SP:func.23">cod</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D26" target="_self" title="COH_SP:def.26">Def30</a></span>;<br/>
<a NAME="E3:79_1_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="coh_sp.html#K24" title="COH_SP:func.24">id$</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1_4"><span class="lab"><font color="Green" title="E53">A14</font></span></a>, <a class="ref" href="coh_sp.html#T47" target="_self" title="COH_SP:th.47">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:79_1_4"/>
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>,<font color="Maroon" title="c8">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79_1"><span class="lab"><font color="Green" title="E50">A11</font></span></a>, <a class="txt" href="#E6:79_1"><span class="lab"><font color="Green" title="E52">A13</font></span></a>, <a class="txt" href="#E1:79_1_4"><span class="lab"><font color="Green" title="E53">A14</font></span></a>, <a class="txt" href="#E2:79_1_4"><span class="lab"><font color="Green" title="E54">A15</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">let </span><font color="Maroon" title="c8">g</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> implies <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> )</span><br/><span class="kw">assume </span><a NAME="E9:79_1"/><span class="lab"><font color="Green" title="E53">A16</font></span>: 
<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font></span><br/><a NAME="E10:79_1"/><span class="lab"><font color="Green" title="E54">A17</font></span>: 
 <a href="coh_sp.html#K22" title="COH_SP:func.22">dom</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D25" target="_self" title="COH_SP:def.25">Def29</a></span>;<br/><a NAME="E11:79_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">g</font> <a href="coh_sp.html#K25" title="COH_SP:func.25">*</a> <span class="p1">(<span class="default"><a href="coh_sp.html#K24" title="COH_SP:func.24">id$</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:79_1"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="ref" href="coh_sp.html#T47" target="_self" title="COH_SP:th.47">Th48</a></span>;<br/><span class="kw">hence </span><a NAME="E12:79_1"/>
<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c8">g</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">b</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79_1"><span class="lab"><font color="Green" title="E50">A11</font></span></a>, <a class="txt" href="#E5:79_1"><span class="lab"><font color="Green" title="E51">A12</font></span></a>, <a class="txt" href="#E9:79_1"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E10:79_1"><span class="lab"><font color="Green" title="E54">A17</font></span></a>, <a class="ref" href="coh_sp.html#D27" target="_self" title="COH_SP:def.27">Def31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:79"/>
 <a href="cat_1.html#G1" title="CAT_1:aggr.1">CatStr</a>(# <span class="p1">(<span class="default"><a href="coh_sp.html#K17" title="COH_SP:func.17">TOL</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K21" title="COH_SP:func.21">MapsT</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K26" title="COH_SP:func.26">fDom</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K27" title="COH_SP:func.27">fCod</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K28" title="COH_SP:func.28">fComp</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="coh_sp.html#K29" title="COH_SP:func.29">fId</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D5" title="CAT_1:def.5">CAT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
