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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_8.html#V7" title="CAT_8:attr.7">with_binary_products</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">c2</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font><br/>  for <font color="Olive" title="b7">f1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</font><br/>  for <font color="Olive" title="b8">f2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b2</font><br/>  for <font color="Olive" title="b9">g1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">c1</font><br/>  for <font color="Olive" title="b10">g2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">c2</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">c2</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="b9">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b10">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b8">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b9">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b7">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b8">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">c1</font>, <font color="Maroon" title="c7">c2</font> be   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font><br/>  for <font color="Olive" title="b2">f2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font><br/>  for <font color="Olive" title="b3">g1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</font><br/>  for <font color="Olive" title="b4">g2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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="b3">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b4">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b2">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">f1</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font><br/>  for <font color="Olive" title="b2">g1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</font><br/>  for <font color="Olive" title="b3">g2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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="b2">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b3">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b1">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Olive" title="b1">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">f2</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</font><br/>  for <font color="Olive" title="b2">g2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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="b1">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b2">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c10">g1</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</font>  st  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Olive" title="b1">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c11">g2</font> be    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span> )</span><br/>











<span class="kw">assume </span><a NAME="E1:115"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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>  or  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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>  or  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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>  or <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:115"/><span class="lab"><font color="Green" title="E68">A2</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c6">c1</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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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>  or  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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>  or <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:115"/><span class="lab"><font color="Green" title="E69">A3</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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>  or <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:115"/><span class="lab"><font color="Green" title="E70">A4</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">c2</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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span></span><br/>

<a NAME="E5:115"/><span class="lab"><font color="Green" title="E71">A5</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">c1</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="ref" href="cat_7.html#T22" onmouseover="rs('cat_7/T22')" onmouseout="rh()">CAT_7:22</a></span>;<br/>
<a NAME="E6:115"/><span class="lab"><font color="Green" title="E72">A6</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">a2</font></span>)</span>,<font color="Maroon" title="c2">a1</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E7:115"/><span class="lab"><font color="Green" title="E73">A7</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c5">b2</font></span>)</span>,<font color="Maroon" title="c4">b1</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E8:115"/><span class="lab"><font color="Green" title="E74">A8</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c7">c2</font></span>)</span>,<font color="Maroon" title="c6">c1</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E9:115"/><span class="lab"><font color="Green" title="E75">A9</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">a2</font></span>)</span>,<font color="Maroon" title="c3">a2</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E10:115"/><span class="lab"><font color="Green" title="E76">A10</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c5">b2</font></span>)</span>,<font color="Maroon" title="c5">b2</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E11:115"/><span class="lab"><font color="Green" title="E77">A11</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c7">c2</font></span>)</span>,<font color="Maroon" title="c7">c2</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#T42" target="_self" onmouseover="rs('cat_8/T42')" onmouseout="rh()">Th42</a></span>;<br/>
<a NAME="E12:115"/><span class="lab"><font color="Green" title="E78">A12</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c3">a2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c5">b2</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E3:115"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="ref" href="cat_8.html#T44" target="_self" onmouseover="rs('cat_8/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E13:115"/><span class="lab"><font color="Green" title="E79">A13</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c5">b2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Maroon" title="c7">c2</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_8.html#T44" target="_self" onmouseover="rs('cat_8/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<a NAME="E14:115"/><span class="lab"><font color="Green" title="E80">A14</font></span>: 
 <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:115"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_7.html#T22" onmouseover="rs('cat_7/T22')" onmouseout="rh()">CAT_7:22</a></span>;<br/>
<span class="lab"><font color="Green" title="E81">A15</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>)</span>)</span> = 
<font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:115"><span class="lab"><font color="Green" title="E72">A6</font></span></a>, <a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
<br/>.= 
<font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E3:115"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="ref" href="cat_8.html#D16" target="_self" onmouseover="rs('cat_8/D16')" onmouseout="rh()">Def16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:115"><span class="lab"><font color="Green" title="E73">A7</font></span></a>, <a class="txt" href="#E12:115"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_8.html#D16" target="_self" onmouseover="rs('cat_8/D16')" onmouseout="rh()">Def16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_8.html#K5" title="CAT_8:func.5">pr1</a> (<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:115"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E13:115"><span class="lab"><font color="Green" title="E79">A13</font></span></a>, <a class="txt" href="#E8:115"><span class="lab"><font color="Green" title="E74">A8</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>)</span>)</span> = 
<font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:115"><span class="lab"><font color="Green" title="E75">A9</font></span></a>, <a class="txt" href="#E3:115"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
<br/>.= 
<font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E67">A1</font></span></a>, <a class="txt" href="#E3:115"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="ref" href="cat_8.html#D16" target="_self" onmouseover="rs('cat_8/D16')" onmouseout="rh()">Def16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:115"><span class="lab"><font color="Green" title="E76">A10</font></span></a>, <a class="txt" href="#E12:115"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="ref" href="cat_8.html#D16" target="_self" onmouseover="rs('cat_8/D16')" onmouseout="rh()">Def16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_8.html#K6" title="CAT_8:func.6">pr2</a> (<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font>)</span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:115"><span class="lab"><font color="Green" title="E78">A12</font></span></a>, <a class="txt" href="#E13:115"><span class="lab"><font color="Green" title="E79">A13</font></span></a>, <a class="txt" href="#E11:115"><span class="lab"><font color="Green" title="E77">A11</font></span></a>, <a class="ref" href="cat_7.html#T23" onmouseover="rs('cat_7/T23')" onmouseout="rh()">CAT_7:23</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E17:115"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c11">g2</font></span>)</span> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <font color="Maroon" title="c9">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g1</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c8">f1</font></span>)</span> <a href="cat_8.html#K7" title="CAT_8:func.7">[x]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g2</font> <a href="cat_7.html#K4" title="CAT_7:func.4">*</a> <font color="Maroon" title="c9">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:115"><span class="lab"><font color="Green" title="E81">A15</font></span></a>, <a class="txt" href="#E14:115"><span class="lab"><font color="Green" title="E80">A14</font></span></a>, <a class="txt" href="#E5:115"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="ref" href="cat_8.html#D16" target="_self" onmouseover="rs('cat_8/D16')" onmouseout="rh()">Def16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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