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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: PRALG_1:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">U1</font>, <font color="Olive" title="b2">U2</font> being   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a>  st <font color="Olive" title="b1">U1</font>,<font color="Olive" title="b2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  holds <br/> for <font color="Olive" title="b3">o1</font> being   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Olive" title="b1">U1</font><br/>  for <font color="Olive" title="b4">o2</font> being   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <font color="Olive" title="b2">U2</font><br/>  for <font color="Olive" title="b5">o</font> being   <a href="unialg_2.html#NM3" title="UNIALG_2:NM.3">operation</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Olive" title="b1">U1</font>,<font color="Olive" title="b2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span><br/>  for <font color="Olive" title="b6">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Olive" title="b1">U1</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b6">n</font> &amp; <font color="Olive" title="b4">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Olive" title="b2">U2</font> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b6">n</font> &amp; <font color="Olive" title="b5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Olive" title="b1">U1</font>,<font color="Olive" title="b2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="partfun1.html#K8" title="PARTFUN1:func.8">.</a> <font color="Olive" title="b6">n</font> &amp; <font color="Olive" title="b6">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Olive" title="b1">U1</font> holds <br/>(  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b3">o1</font> &amp;  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K18" title="MARGREL1:func.18">arity</a> <font color="Olive" title="b4">o2</font> &amp; <font color="Olive" title="b5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pralg_1.html#K3" title="PRALG_1:func.3">[[:</a><span class="default"><font color="Olive" title="b3">o1</font>,<font color="Olive" title="b4">o2</font></span><a href="pralg_1.html#K3" title="PRALG_1:func.3">:]]</a></span> )</div></div>
