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<span class="kw">let </span><font color="Maroon" title="c1">UA</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span><br/> for <font color="Olive" title="b2">f</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="endalg.html#K1" title="ENDALG:func.1">UAEnd</a> <font color="Maroon" title="c1">UA</font>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="endalg.html#K1" title="ENDALG:func.1">UAEnd</a> <font color="Maroon" title="c1">UA</font>  st <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Olive" title="b1">f</font> holds <br/><font color="Maroon" title="c2">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="endalg.html#K1" title="ENDALG:func.1">UAEnd</a> <font color="Maroon" title="c1">UA</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">f</font> implies <font color="Maroon" title="c2">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:18"/>
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span></span><br/>

<a NAME="E2:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msuhom_1.html#D3" title="MSUHOM_1:def.3">MSUHOM_1:def 3</a></span>;<br/>
<a NAME="E3:18"/>
<font color="Maroon" title="c3">f</font> <a href="alg_1.html#R1" title="ALG_1:pred.1">is_homomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="endalg.html#D1" target="_self" title="ENDALG:def.1">Def1</a></span>;<br/>
<a NAME="E4:18"/><span class="kw">then </span>
 <a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">f</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span> <a href="msuhom_1.html#K1" title="MSUHOM_1:func.1">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">UA</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msuhom_1.html#T16" title="MSUHOM_1:th.16">MSUHOM_1:16</a></span>;<br/>
<a NAME="E5:18"/><span class="kw">then </span>
<font color="Maroon" title="c2">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font>, <a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="msuhom_1.html#T9" title="MSUHOM_1:th.9">MSUHOM_1:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:18"/>
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="endalg.html#D4" target="_self" title="ENDALG:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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