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<div>:: <span class="kw">deftheorem </span>   defines <a href="scmring1.html#K8" title="SCMRING1:func.8">SCM-Exec</a> <a onclick="hs(this)" href="javascript:()">SCMRING1:def 15 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="funct_2.html#NM5" title="FUNCT_2:NM.5">Action</a> of <span class="p1">(<span class="default"><a href="scmringi.html#K1" title="SCMRINGI:func.1">SCM-Instr</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-VAL</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-OK</a></span>)</span></span>)</span> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring1.html#K8" title="SCMRING1:func.8">SCM-Exec</a> <font color="Olive" title="b1">R</font> iff  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmringi.html#K1" title="SCMRINGI:func.1">SCM-Instr</a> <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">y</font> being   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Olive" title="b1">R</font> holds  <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring1.html#K7" title="SCMRING1:func.7">SCM-Exec-Res</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) );<br/></span></div>
