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<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>  st <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  holds <br/> <a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Olive" title="b1">h</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  implies  <a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Maroon" title="c3">h</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</span><br/>





<b>assume </b><a NAME="E1:23"/>
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Maroon" title="c3">h</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<a NAME="E2:23"/><b>then </b>
 <a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Maroon" title="c3">h</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">h</font>
 
<b>by </b><i><a class="ref" href="msuhom_1.html#D3" target="_self" title="MSUHOM_1:def.3">Def3</a>, <a class="ref" href="msuhom_1.html#T10" target="_self" title="MSUHOM_1:th.10">Th10</a></i>;<br/>
<a NAME="E3:23"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>hence </b><a NAME="E4:23"/>
 <a href="msuhom_1.html#K3" title="MSUHOM_1:func.3">MSAlg</a> <font color="Maroon" title="c3">h</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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