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<b>consider </b><font color="Maroon" title="c1">D1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:13_1"/><i><font color="Green" title="E18">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c2">D2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:13_1"/><i><font color="Green" title="E19">A4</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c3">D3</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:13_1"/><i><font color="Green" title="E20">A5</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c4">f1</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E8:13_1"/><i><font color="Green" title="E21">A6</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D1</font>
 <b>and </b><br/><a NAME="E9:13_1"/><i><font color="Green" title="E22">A7</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">D1</font> holds <br/><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">x</font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3" title="FUNCT_1:sch.3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c5">f2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E11:13_1"/><i><font color="Green" title="E23">A8</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D2</font>
 <b>and </b><br/><a NAME="E12:13_1"/><i><font color="Green" title="E24">A9</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="c2">D2</font> holds <br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">x</font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3" title="FUNCT_1:sch.3">FUNCT_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c6">f3</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E14:13_1"/><i><font color="Green" title="E25">A10</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D3</font>
 <b>and </b><br/><a NAME="E15:13_1"/><i><font color="Green" title="E26">A11</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="c3">D3</font> holds <br/><font color="Maroon" title="c6">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">x</font>)
 <b>from </b><i><a class="ref" href="funct_1.html#S3" title="FUNCT_1:sch.3">FUNCT_1:sch 3</a>();<br/></i>
<b>set </b><font color="Maroon" title="c7">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font>;<br/>
<b>take </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive" title="b1">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">c</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">c</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">c</font>) ) ) ) )</span><br/>

<i><font color="Green" title="E27">A12</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
;<br/>
<b>thus </b><a NAME="E17:13_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
  <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="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">c</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">c</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Olive" title="b1">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">c</font>) ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:13_1_2"/><i><font color="Green" title="E28">A13</font></i>: 
<font color="Maroon" title="c1">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )</span><br/>

<b>thus </b><a NAME="E1:13_1_2_1"/>
(  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:13_1"><i><font color="Green" title="E18">A3</font></i></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><b>end;</b></div>
<a NAME="E2:13_1_2"/>
<font color="Maroon" title="c2">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )</span><br/>

<b>thus </b><a NAME="E1:13_1_2_2"/>
(  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:13_1"><i><font color="Green" title="E19">A4</font></i></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><b>end;</b></div>
<a NAME="E3:13_1_2"/><b>then </b><i><font color="Green" title="E29">A14</font></i>: 
<font color="Maroon" title="c1">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="txt" href="recdef_2.html#E1:13_1_2"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E4:13_1_2"/>
<font color="Maroon" title="c3">D3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )</span><br/>

<b>thus </b><a NAME="E1:13_1_2_3"/>
(  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:13_1"><i><font color="Green" title="E20">A5</font></i></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><b>end;</b></div>
<b>hence </b><a NAME="E5:13_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:13_1"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="recdef_2.html#E11:13_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="recdef_2.html#E14:13_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="txt" href="recdef_2.html#E16:13_1"><i><font color="Green" title="E27">A12</font></i></a>, <a class="txt" href="recdef_2.html#E3:13_1_2"><i><font color="Green" title="E29">A14</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">F<sub>1</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E6:13_1_2"/><i><font color="Green" title="E30">A15</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span></span><br/>

<a NAME="E7:13_1_2"/><b>then </b>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c8">x</font>] or <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">x</font>] or <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">x</font>] )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E2:13"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>
<a NAME="E8:13_1_2"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font> )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E2:13_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="recdef_2.html#E4:13_1"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="recdef_2.html#E6:13_1"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="recdef_2.html#E6:13_1_2"><i><font color="Green" title="E30">A15</font></i></a></i>;<br/>
<a NAME="E9:13_1_2"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">D2</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E10:13_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span>
 <b>by </b><i><a class="txt" href="recdef_2.html#E8:13_1"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="recdef_2.html#E11:13_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="recdef_2.html#E14:13_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="txt" href="recdef_2.html#E16:13_1"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</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><b>end;</b></div>

<b>let </b><font color="Maroon" title="c8">c</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"> ( <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() implies ( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c8">c</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c8">c</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>) ) ) )</span><br/>

<b>assume </b><a NAME="E18:13_1"/><i><font color="Green" title="E28">A16</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c8">c</font>) ) &amp; ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c8">c</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>) ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c8">c</font>) ) &amp; ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>) ) )</span>
<div class="add"><b>assume </b><a NAME="E1:13_1_3"/><i><font color="Green" title="E29">A17</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c8">c</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c8">c</font>)</span><br/><a NAME="E2:13_1_3"/><b>then </b><i><font color="Green" title="E30">A18</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D1</font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:13_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a></i>;<br/><a NAME="E3:13_1_3"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">c</font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:13"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a>, <a class="txt" href="recdef_2.html#E1:13_1_3"><i><font color="Green" title="E29">A17</font></i></a></i>;<br/><a NAME="E4:13_1_3"/><b>then </b><i><font color="Green" title="E31">A19</font></i>: 
not <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:13_1"><i><font color="Green" title="E19">A4</font></i></a></i>;<br/><a NAME="E5:13_1_3"/>
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:13"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a>, <a class="txt" href="recdef_2.html#E1:13_1_3"><i><font color="Green" title="E29">A17</font></i></a></i>;<br/><a NAME="E6:13_1_3"/><b>then </b>
not <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:13_1"><i><font color="Green" title="E20">A5</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="recdef_2.html#E14:13_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="recdef_2.html#E11:13_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="recdef_2.html#E4:13_1_3"><i><font color="Green" title="E31">A19</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c8">c</font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E9:13_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="txt" href="recdef_2.html#E2:13_1_3"><i><font color="Green" title="E30">A18</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>] implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>) )</span>
<div class="add"><b>assume </b><a NAME="E1:13_1_4"/><i><font color="Green" title="E29">A20</font></i>: 
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c8">c</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c8">c</font>)</span><br/><a NAME="E2:13_1_4"/><b>then </b><i><font color="Green" title="E30">A21</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D2</font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E4:13_1"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a></i>;<br/><a NAME="E3:13_1_4"/>
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>]
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:13"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a>, <a class="txt" href="recdef_2.html#E1:13_1_4"><i><font color="Green" title="E29">A20</font></i></a></i>;<br/><a NAME="E4:13_1_4"/><b>then </b>
not <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font>
 <b>by </b><i><a class="txt" href="recdef_2.html#E6:13_1"><i><font color="Green" title="E20">A5</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="recdef_2.html#E14:13_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="recdef_2.html#E11:13_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="recdef_2.html#E2:13_1_4"><i><font color="Green" title="E30">A21</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c8">c</font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E12:13_1"><i><font color="Green" title="E24">A9</font></i></a>, <a class="txt" href="recdef_2.html#E2:13_1_4"><i><font color="Green" title="E30">A21</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E21:13_1"/>
<font color="Maroon">P<sub>3</sub></font>[<font color="Maroon" title="c8">c</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>)</span><br/>

<a NAME="E22:13_1"/><b>then </b><i><font color="Green" title="E29">A22</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D3</font>
 
<b>by </b><i><a class="txt" href="recdef_2.html#E6:13_1"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="recdef_2.html#E18:13_1"><i><font color="Green" title="E28">A16</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">f3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> = 
<font color="Maroon" title="c6">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>
<b>by </b><i><a class="txt" href="recdef_2.html#E14:13_1"><i><font color="Green" title="E25">A10</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c8">c</font>)
<b>by </b><i><a class="txt" href="recdef_2.html#E15:13_1"><i><font color="Green" title="E26">A11</font></i></a>, <a class="txt" href="recdef_2.html#E22:13_1"><i><font color="Green" title="E29">A22</font></i></a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
