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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"> ( <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="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font> )</span><br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E9">A1</font></i>: 
<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="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">f</font> = <span class="p1">(<span class="default"><a href="pboole.html#K8" title="PBOOLE:func.8">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span>,<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7" title="MSUALG_1:th.7">MSUALG_1:7</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green" title="E10">A2</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</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> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D13" title="MSUALG_1:def.13">MSUALG_1:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f</font> = <span class="p1">(<span class="default"><a href="pboole.html#K8" title="PBOOLE:func.8">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>,<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7" title="MSUALG_1:th.7">MSUALG_1:7</a></i>;<br/>
<a NAME="E5:13"/><i><font color="Green" title="E11">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</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> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c4">f</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D13" title="MSUALG_1:def.13">MSUALG_1:def 13</a></i>;<br/>
<a NAME="E6:13"/><b>then </b>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="msuhom_1.html#E3:13"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:13"/>
 <a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K7" title="MSUALG_1:func.7">MSSign</a> <font color="Maroon" title="c2">U2</font>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="msuhom_1.html#E3:13"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="msuhom_1.html#E5:13"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</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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