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<div><span class="kw">theorem </span><a NAME="T78"><span class="comment"><font color="firebrick">:: CAT_4:78</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</font>, <font color="Olive" title="b6">e</font>, <font color="Olive" title="b7">s</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font><br/>  for <font color="Olive" title="b8">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font><br/>  for <font color="Olive" title="b9">h</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">d</font><br/>  for <font color="Olive" title="b10">g</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b4">c</font>,<font color="Olive" title="b6">e</font><br/>  for <font color="Olive" title="b11">k</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b5">d</font>,<font color="Olive" title="b7">s</font>  st  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">d</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b4">c</font>,<font color="Olive" title="b6">e</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Olive" title="b5">d</font>,<font color="Olive" title="b7">s</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b10">g</font> <a href="cat_4.html#K31" title="CAT_4:func.31">+</a> <font color="Olive" title="b11">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">f</font> <a href="cat_4.html#K31" title="CAT_4:func.31">+</a> <font color="Olive" title="b9">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b8">f</font></span>)</span> <a href="cat_4.html#K31" title="CAT_4:func.31">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b11">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b9">h</font></span>)</span></div></div>
