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<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font>;<br/><b>let </b><font color="Maroon" title="c6">F</font> be    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c1">I</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:92"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="cat_3.html#R3" title="CAT_3:pred.3">is_a_coproduct_wrt</a> <font color="Maroon" title="c6">F</font>
 <b>and </b><br/><a NAME="E2:92"/><i><font color="Green" title="E55">A2</font></i>: 
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>and </b><br/><a NAME="E3:92"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 ;<br/>

<b>thus </b><a NAME="E4:92"/>
<font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="cat_3.html#T72" target="_self" title="CAT_3:th.72">Th72</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D18" target="_self" title="CAT_3:def.18">CAT_3:def 18</a><br/>

<b>let </b><font color="Maroon" title="c7">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C</font>;<br/><b>let </b><font color="Maroon" title="c8">F'</font> be    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c1">I</font>;<br/>



<b>assume </b><a NAME="E5:92"/><i><font color="Green" title="E57">A4</font></i>: 
 <a href="cat_3.html#K3" title="CAT_3:func.3">doms</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cat_3.html#K3" title="CAT_3:func.3">doms</a> <font color="Maroon" title="c8">F'</font>
 ;<br/>

<a NAME="E6:92"/>
 <a href="cat_3.html#K4" title="CAT_3:func.4">cods</a> <font color="Maroon" title="c6">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">I</font> <a href="cat_3.html#K1" title="CAT_3:func.1">--&gt;</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="cat_3.html#D17" target="_self" title="CAT_3:def.17">Def17</a></i>;<br/>
<a NAME="E7:92"/><b>then </b>
 <a href="cat_3.html#K3" title="CAT_3:func.3">doms</a> <font color="Maroon" title="c6">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cat_3.html#K3" title="CAT_3:func.3">doms</a> <font color="Maroon" title="c8">F'</font>
 
<b>by </b><i><a class="txt" href="cat_3.html#E5:92"><i><font color="Green" title="E57">A4</font></i></a>, <a class="ref" href="cat_3.html#T21" target="_self" title="CAT_3:th.21">Th21</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">h</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font><b> such that </b><br/><a NAME="E9:92"/><i><font color="Green" title="E58">A5</font></i>: 
<font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 <b>and </b><br/><a NAME="E10:92"/><i><font color="Green" title="E59">A6</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> holds <br/>( ( for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Olive" title="b1">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F'</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b2">x</font> ) iff <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> )
 <b>by </b><i><a class="txt" href="cat_3.html#E1:92"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="cat_3.html#D18" target="_self" title="CAT_3:def.18">Def18</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font><b> such that </b><br/><a NAME="E12:92"/><i><font color="Green" title="E60">A7</font></i>: 
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font> )
 <b>and </b><br/><a NAME="E13:92"/><i><font color="Green" title="E61">A8</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">f</font></span>)</span>
 <b>and </b><br/><a NAME="E14:92"/><i><font color="Green" title="E62">A9</font></i>: 
<font color="Maroon" title="c10">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="cat_3.html#E3:92"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="cat_1.html#D12" title="CAT_1:def.12">CAT_1:def 12</a></i>;<br/>
<b>take </b><font color="Maroon" title="c11">hg</font> = <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font>;<br/>

<a NAME="E15:92"/><i><font color="Green" title="E63">A10</font></i>: 
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> )
 
<b>by </b><i><a class="txt" href="cat_3.html#E9:92"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>;<br/>
<a NAME="E16:92"/><b>then </b>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E12:92"><i><font color="Green" title="E60">A7</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/>
<b>hence </b><a NAME="E17:92"/>
<font color="Maroon" title="c11">hg</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">c</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c12">k</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font>;<br/>

<b>assume </b><a NAME="E18:92"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">c</font>
 ;<br/>

<a NAME="E19:92"/><b>then </b><i><font color="Green" title="E64">A11</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>;<br/>
<b>thus </b><a NAME="E20:92"/>
( ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F'</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">x</font> ) implies <font color="Maroon" title="c11">hg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">k</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:92_1"/><i><font color="Green" title="E65">A12</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">F'</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1_1"><b>now </b></a><div class="add"><a NAME="E1:92_1_1"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E19:92"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/><b>hence </b><a NAME="E2:92_1_1"/>
<font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 ;<br/><b>let </b><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E3:92_1_1"/><i><font color="Green" title="E66">A13</font></i>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/><a NAME="E4:92_1_1"/><b>then </b>
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="cat_3.html#T67" target="_self" title="CAT_3:th.67">Th67</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span> = 
<font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E19:92"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E3:92_1_1"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="cat_3.html#D8" target="_self" title="CAT_3:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c8">F'</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font>
<b>by </b><i><a class="txt" href="cat_3.html#E1:92_1"><i><font color="Green" title="E65">A12</font></i></a>, <a class="txt" href="cat_3.html#E3:92_1_1"><i><font color="Green" title="E66">A13</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E3:92_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c10">g</font>
 
<b>by </b><i><a class="txt" href="cat_3.html#E10:92"><i><font color="Green" title="E59">A6</font></i></a></i>;<br/>
<b>hence </b><font color="Maroon" title="c11">hg</font> = 
<font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E12:92"><i><font color="Green" title="E60">A7</font></i></a>, <a class="txt" href="cat_3.html#E13:92"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="cat_3.html#E19:92"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c12">k</font>
<b>by </b><i><a class="txt" href="cat_3.html#E19:92"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="cat_1.html#T47" title="CAT_1:th.47">CAT_1:47</a></i>
;<br/><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E21:92"/><i><font color="Green" title="E65">A14</font></i>: 
<font color="Maroon" title="c11">hg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">k</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E22:92"/><i><font color="Green" title="E66">A15</font></i>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/>

<a NAME="E23:92"/><b>then </b><i><font color="Green" title="E67">A16</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="cat_3.html#T67" target="_self" title="CAT_3:th.67">Th67</a></i>;<br/>
<a NAME="E24:92"/><b>then </b><i><font color="Green" title="E68">A17</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_3.html#K8" title="CAT_3:func.8">*</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span> = 
<font color="Maroon" title="c12">k</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E22:92"><i><font color="Green" title="E66">A15</font></i></a>, <a class="ref" href="cat_3.html#D8" target="_self" title="CAT_3:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E12:92"><i><font color="Green" title="E60">A7</font></i></a>, <a class="txt" href="cat_3.html#E15:92"><i><font color="Green" title="E63">A10</font></i></a>, <a class="txt" href="cat_3.html#E21:92"><i><font color="Green" title="E65">A14</font></i></a>, <a class="txt" href="cat_3.html#E24:92"><i><font color="Green" title="E68">A17</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E12:92"><i><font color="Green" title="E60">A7</font></i></a>, <a class="txt" href="cat_3.html#E14:92"><i><font color="Green" title="E62">A9</font></i></a>, <a class="txt" href="cat_3.html#E23:92"><i><font color="Green" title="E67">A16</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c9">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font></span>)</span>
<b>by </b><i><a class="txt" href="cat_3.html#E2:92"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="cat_3.html#E23:92"><i><font color="Green" title="E67">A16</font></i></a>, <a class="ref" href="cat_1.html#T46" title="CAT_1:th.46">CAT_1:46</a></i>
<br/>.= 
<font color="Maroon" title="c8">F'</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c13">x</font>
<b>by </b><i><a class="txt" href="cat_3.html#E9:92"><i><font color="Green" title="E58">A5</font></i></a>, <a class="txt" href="cat_3.html#E10:92"><i><font color="Green" title="E59">A6</font></i></a>, <a class="txt" href="cat_3.html#E22:92"><i><font color="Green" title="E66">A15</font></i></a></i>
;<br/>


</div>
