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<a NAME="E1:177_1_1"/><i><font color="Green" title="E68">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></i>;<br/>
<a NAME="E2:177_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">IL</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D40" target="_self" title="AMI_1:def.40">Def40</a></i>;<br/>
<a NAME="E3:177_1_1"/><b>then </b><i><font color="Green" title="E69">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">IL</font>
 
<b>by </b><i><a class="txt" href="#E1:177_1_1"><i><font color="Green" title="E68">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:177_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</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" title="c3">S</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:177_1_1"/><b>then </b>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">s</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> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T80" target="_self" title="AMI_1:th.80">Th80</a></i>;<br/>
<a NAME="E6:177_1_1"/><b>then </b><i><font color="Green" title="E70">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="txt" href="#E1:177_1_1"><i><font color="Green" title="E68">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</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="c6">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"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/><b>assume </b><a NAME="E1:177_1_1_1"/><i><font color="Green" title="E71">A4</font></i>: 
<font color="Maroon" title="c6">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"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span>
 ; <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"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/><b>then reconsider </b><font color="Maroon" title="c7">l</font> = <font color="Maroon" title="c6">x</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font> <b>by </b><i><a class="txt" href="#E3:177_1_1"><i><font color="Green" title="E69">A2</font></i></a>, <a class="ref" href="ami_1.html#D4" target="_self" title="AMI_1:def.4">Def4</a></i>;<br/><a NAME="E3:177_1_1_1"/><i><font color="Green" title="E72">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:177_1_1_1"><i><font color="Green" title="E71">A4</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:177_1_1_1"/><i><font color="Green" title="E73">A6</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/><a NAME="E5:177_1_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></i>;<br/><a NAME="E6:177_1_1_1"/><b>then </b><i><font color="Green" title="E74">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="txt" href="#E4:177_1_1_1"><i><font color="Green" title="E73">A6</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">l</font> = 
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c7">l</font>

<br/>.= 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c3">S</font>
<b>by </b><i><a class="ref" href="ami_1.html#D14" target="_self" title="AMI_1:def.14">Def14</a></i>
;<br/><b>hence </b><a NAME="E8:177_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="#E3:177_1_1_1"><i><font color="Green" title="E72">A5</font></i></a>, <a class="txt" href="#E6:177_1_1_1"><i><font color="Green" title="E74">A7</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>then reconsider </b><font color="Maroon" title="c6">fs</font> = <font color="Maroon" title="c5">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">s</font> as   <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</a> of <font color="Maroon" title="c3">S</font> <b>by </b><i><a class="txt" href="#E6:177_1_1"><i><font color="Green" title="E70">A3</font></i></a>, <a class="ref" href="card_3.html#D9" title="CARD_3:def.9">CARD_3:def 9</a></i>;<br/>
<a NAME="E9:177_1_1"/>
<font color="Maroon" title="c6">fs</font> is <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a>
 
<b>by </b><i><a class="txt" href="#E3:177_1_1"><i><font color="Green" title="E69">A2</font></i></a>, <a class="ref" href="ami_1.html#D40" target="_self" title="AMI_1:def.40">Def40</a></i>;<br/>
<b>hence </b><a NAME="E10:177_1_1"/>
<font color="Maroon" title="c4">s</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c5">f</font> is  <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> <a href="ami_1.html#NM7" title="AMI_1:NM.7">PartState</a> of <font color="Maroon" title="c3">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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