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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">LAST05</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: AESCIP_1:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">SBT</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default">8 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span><br/>  for <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">text</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 4 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default">4 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p2">(<span class="default">8 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span></span>)</span><br/>  for <font color="Olive" title="b4">key</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b2">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default">4 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p2">(<span class="default">8 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span></span>)</span><br/>  for <font color="Olive" title="b5">dkeyi</font>, <font color="Olive" title="b6">ekeyi</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 4 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default">4 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p2">(<span class="default">8 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span></span>)</span>  st ( <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 ) &amp; <font color="Olive" title="b5">dkeyi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="aescip_1.html#K15" title="AESCIP_1:func.15">KeyExpansion</a> (<font color="Olive" title="b1">SBT</font>,<font color="Olive" title="b2">m</font>)</span>)</span> <a href="aescip_1.html#K1" title="AESCIP_1:func.1">.</a> <font color="Olive" title="b4">key</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b6">ekeyi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="descip_1.html#K1" title="DESCIP_1:func.1">Rev</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="aescip_1.html#K15" title="AESCIP_1:func.15">KeyExpansion</a> (<font color="Olive" title="b1">SBT</font>,<font color="Olive" title="b2">m</font>)</span>)</span> <a href="aescip_1.html#K1" title="AESCIP_1:func.1">.</a> <font color="Olive" title="b4">key</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">m</font></span>)</span> holds <br/><a href="aescip_1.html#K8" title="AESCIP_1:func.8">AddRoundKey</a> <a href="aescip_1.html#K2" title="AESCIP_1:func.2">.</a> (<span class="p1">(<span class="default"><a href="aescip_1.html#K8" title="AESCIP_1:func.8">AddRoundKey</a> <a href="aescip_1.html#K2" title="AESCIP_1:func.2">.</a> (<font color="Olive" title="b3">text</font>,<font color="Olive" title="b6">ekeyi</font>)</span>)</span>,<font color="Olive" title="b5">dkeyi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">text</font></div></div>
