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<a NAME="E1:29_1"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></span>;<br/>
<a NAME="E2:29_1"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>()
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#D11" title="ALTCAT_2:def.11">ALTCAT_2:def 11</a></span>;<br/>
<a NAME="E3:29_1"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="kw">hereby </span> <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>()</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>() )</span><br/><span class="kw">assume </span><a NAME="E1:29_1_1_1"/><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>()</span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">a</font> = <font color="Maroon" title="c1">x</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>1</sub></font>() <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E1:29_1_1_1"><span class="lab"><font color="Green" title="E27">A8</font></span></a></span>;<br/><a NAME="E4:29_1_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">a</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/><a NAME="E5:29_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> is   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>3</sub></font>()
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E22">A3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:29_1_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>() or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() )</span><br/>

<span class="kw">assume </span><a NAME="E2:29_1_1"/><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>()</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">a</font> = <font color="Maroon" title="c1">x</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>3</sub></font>() ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>1</sub></font>() <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29_1"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E2:29_1_1"><span class="lab"><font color="Green" title="E27">A9</font></span></a></span>;<br/>
<a NAME="E5:29_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">a</font>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E22">A3</font></span></a></span>;<br/>
<a NAME="E6:29_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> is   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>2</sub></font>()
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:29_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>3</sub></font>() <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c3">x1</font> = <font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c4">y1</font> = <font color="Maroon" title="c2">b</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c5">x2</font> = <font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c6">y2</font> = <font color="Maroon" title="c4">y1</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>3</sub></font>() <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1"><span class="lab"><font color="Green" title="E26">A7</font></span></a></span>;<br/><a NAME="E3:29_1_2"/>
( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon" title="c4">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() )
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">a9</font> = <font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c8">b9</font> = <font color="Maroon" title="c2">b</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon">F<sub>1</sub></font>() <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E24">A5</font></span></a></span>;<br/><a NAME="E5:29_1_2"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></span>;<br/><a NAME="E6:29_1_2"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> or <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:29_1_2_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">f</font> = <font color="Maroon" title="c9">f</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:29_1_2"><span class="lab"><font color="Green" title="E27">A10</font></span></a></span>;<br/>
<a NAME="E3:29_1_2_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c10">f</font>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E5:29_1_2"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E1:29_1_2_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:29_1_2_1"/>
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E5:29_1_2"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E1:29_1_2_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:29_1_2"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></span>;<br/><a NAME="E8:29_1_2"/>
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> or <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:29_1_2_2"/><span class="lab"><font color="Green" title="E30">A14</font></span>: 
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">y1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">f</font> = <font color="Maroon" title="c9">f</font> as   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:29_1_2"><span class="lab"><font color="Green" title="E29">A13</font></span></a></span>;<br/>
<a NAME="E3:29_1_2_2"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c7">a9</font>,<font color="Maroon" title="c8">b9</font>,<font color="Maroon" title="c10">f</font>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E7:29_1_2"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E1:29_1_2_2"><span class="lab"><font color="Green" title="E30">A14</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:29_1_2_2"/>
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E7:29_1_2"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E1:29_1_2_2"><span class="lab"><font color="Green" title="E30">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E9:29_1_2"/>
the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>3</sub></font>() <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:29_1_2"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:29_1"/>
 <a href="altcat_1.html#G2" title="ALTCAT_1:aggr.2">AltCatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon">F<sub>2</sub></font>() #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#G2" title="ALTCAT_1:aggr.2">AltCatStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>3</sub></font>(),the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon">F<sub>3</sub></font>(),the <a href="altcat_1.html#U2" title="ALTCAT_1:sel.2">Comp</a> of <font color="Maroon">F<sub>3</sub></font>() #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="altcat_1.html#T9" title="ALTCAT_1:th.9">ALTCAT_1:9</a>, <a class="ref" href="altcat_2.html#T27" title="ALTCAT_2:th.27">ALTCAT_2:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
