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<div>:: <span class="kw">deftheorem </span>   defines <a href="mazurulm.html#V3" title="MAZURULM:attr.3">midpoints-preserving</a> <a onclick="hs(this)" href="javascript:()">MAZURULM:def 3 : <br/></a><span> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</a> <br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="mazurulm.html#V3" title="MAZURULM:attr.3">midpoints-preserving</a>  iff  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">E</font> holds  <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> 2</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b5">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="xxreal_3.html#K6" title="XXREAL_3:func.6">/</a> 2</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">b</font></span>)</span></span>)</span> );<br/></span></div>
