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<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: GROUP_23:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="group_19.html#NM1" title="GROUP_19:NM.1">Group-Family</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">G</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Olive" title="b2">F</font><br/>  for <font color="Olive" title="b4">S</font> being   <a href="group_23.html#NM2" title="GROUP_23:NM.2">Subgroup-Family</a> of <font color="Olive" title="b2">F</font>  st (  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> holds  <font color="Olive" title="b4">S</font> <a href="group_23.html#K4" title="GROUP_23:func.4">.</a> <font color="Olive" title="b5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b5">i</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="group_23.html#K9" title="GROUP_23:func.9">incl</a> <font color="Olive" title="b3">G</font></span>)</span></span>)</span> ) holds <br/> for <font color="Olive" title="b5">f</font> being    <a href="group_23.html#M1" title="GROUP_23:mode.1">Homomorphism-Family</a> of <font color="Olive" title="b3">G</font>,<font color="Olive" title="b4">S</font>  st (  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> holds  <font color="Olive" title="b5">f</font> <a href="group_23.html#K10" title="GROUP_23:func.10">.</a> <font color="Olive" title="b6">i</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <span class="p1">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b6">i</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_23.html#K9" title="GROUP_23:func.9">incl</a> <font color="Olive" title="b3">G</font></span>)</span> ) holds <br/> <a href="group_23.html#K13" title="GROUP_23:func.13">product</a> <font color="Olive" title="b5">f</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">G</font></div></div>
