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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">B</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>  st <font color="Olive" title="b3">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Olive" title="b1">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Olive" title="b3">F</font></span>)</span>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b3">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon" title="c1">S</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="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>  st <font color="Olive" title="b1">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Olive" title="b1">F</font></span>)</span>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> implies <span class="p1">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c4">F</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:40"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</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"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c4">F</font></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="40_1"><span class="kw">now </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">  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span></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> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> )</span><br/><span class="kw">assume </span><a NAME="E1:40_1"/>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</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"><span class="p2">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">s</font> = <font color="Maroon" title="c5">i</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">h</font> =  <a href="msualg_4.html#K18" title="MSUALG_4:func.18">MSHomQuot</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c6">s</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K4" title="MSUALG_4:func.4">Class</a> <span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">f</font> = <font color="Maroon" title="c7">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K14" title="MSUALG_4:func.14">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> ;<br/><a NAME="E5:40_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 for <font color="Olive" title="b1">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> holds  <font color="Maroon" title="c8">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="40_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c8">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font> = 
<font color="Maroon" title="c7">h</font> <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="msualg_4.html#K14" title="MSUALG_4:func.14">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<br/>.= 
<font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c9">c</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_4.html#D15" onmouseover="rs('msualg_4/D15')" onmouseout="rh()">MSUALG_4:def 15</a></span>
<br/>.= 
<font color="Maroon" title="c7">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p2">(<span class="default"><a href="msualg_4.html#K16" title="MSUALG_4:func.16">MSCng</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<font color="Maroon" title="c9">c</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="msualg_4.html#D18" onmouseover="rs('msualg_4/D18')" onmouseout="rh()">MSUALG_4:def 18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="msualg_4.html#D19" onmouseover="rs('msualg_4/D19')" onmouseout="rh()">MSUALG_4:def 19</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><span class="kw">end;</span></div><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T2" onmouseover="rs('msualg_3/T2')" onmouseout="rh()">MSUALG_3:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_4.html#K18" title="MSUALG_4:func.18">MSHomQuot</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p3">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_4.html#D20" onmouseover="rs('msualg_4/D20')" onmouseout="rh()">MSUALG_4:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_4.html#K18" title="MSUALG_4:func.18">MSHomQuot</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c6">s</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K14" title="MSUALG_4:func.14">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c6">s</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_4.html#D16" onmouseover="rs('msualg_4/D16')" onmouseout="rh()">MSUALG_4:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:40_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:40"/>
<span class="p1">(<span class="default"><a href="msualg_4.html#K19" title="MSUALG_4:func.19">MSHomQuot</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_4.html#K15" title="MSUALG_4:func.15">MSNat_Hom</a> (<font color="Maroon" title="c2">A</font>,<span class="p2">(<span class="default"><a href="msualg_4.html#K17" title="MSUALG_4:func.17">MSCng</a> <font color="Maroon" title="c4">F</font></span>)</span>)</span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c4">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"> verum</span><br/>


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