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<b>let </b><font color="Maroon" title="c1">o</font>, <font color="Maroon" title="c2">m</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span><br/> for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> holds  <font color="Olive" title="b1">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font></span><br/><b>let </b><font color="Maroon" title="c3">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> holds  <font color="Maroon" title="c3">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font></span><br/><b>let </b><font color="Maroon" title="c4">p1</font>, <font color="Maroon" title="c5">p2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">c</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font></span><br/>







<b>thus </b><a NAME="E1:17"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c4">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> )
 <b>by </b><i><a class="ref" href="cat_4.html#T4" target="_self" title="CAT_4:th.4">Th4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D16" title="CAT_3:def.16">CAT_3:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span><br/> for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p1</font></span>)</span> or  not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">p2</font></span>)</span> or  ex <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> st <br/>( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c3">c</font> &amp; ( for <font color="Olive">b<sub>5</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>3</sub></font> or <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>5</sub></font> ) &amp; (  not <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>5</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>3</sub></font> ) ) ) ) ) ) )</span><br/>

<b>let </b><font color="Maroon" title="c6">d</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p1</font></span>)</span> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">p2</font></span>)</span> or  ex <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>4</sub></font> ) &amp; (  not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>4</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) ) ) ) ) ) )</span><br/><b>let </b><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p1</font></span>)</span> or  not <font color="Maroon" title="c8">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">p2</font></span>)</span> or  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; (  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) ) ) ) )</span><br/>



<b>assume </b><a NAME="E2:17"/>
( <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c4">p1</font></span>)</span> &amp; <font color="Maroon" title="c8">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">p2</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; (  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) ) ) )</span><br/>

<b>take </b><font color="Maroon" title="c9">h</font> = <font color="Maroon" title="c4">p1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  not <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) ) ) )</span><br/>

<b>thus </b><a NAME="E3:17"/>
<font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="ref" href="cat_4.html#T7" target="_self" title="CAT_4:th.7">Th7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  not <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) )</span><br/>

<b>thus </b><a NAME="E4:17"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">c</font> or ( (  not <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  not <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or ( <font color="Maroon" title="c4">p1</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) )
 <b>by </b><i><a class="ref" href="cat_4.html#T6" target="_self" title="CAT_4:th.6">Th6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
