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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/>  for <font color="Olive" title="b2">p</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">d</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b3">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Olive" title="b2">p</font> iff <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">d</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds <br/> ( <font color="Olive" title="b2">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Olive" title="b1">p</font> iff <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   non  <a href="compos_1.html#V2" title="COMPOS_1:attr.2">halt-free</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">d</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds <br/> ( <font color="Olive" title="b1">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> iff <font color="Maroon" title="c3">p</font>,<font color="Olive" title="b1">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">d</font> be   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> iff <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )</span><br/>







<span class="kw">thus </span><a NAME="E1:41"/>
( <font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> implies <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> implies <font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:41_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:41_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D14" target="_self" title="EXTPRO_1:def.14">EXTPRO_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">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"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> implies  ex <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font></span>)</span>) ) )</span><br/>

<span class="kw">assume </span><a NAME="E3:41_1"/>
<font color="Maroon" title="c5">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"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font></span>)</span>) )</span><br/>

<a NAME="E4:41_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">s</font> = <font color="Maroon" title="c5">x</font> as   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T104" title="FUNCT_1:th.104">FUNCT_1:104</a>, <a class="ref" href="relat_1.html#T171" title="RELAT_1:th.171">RELAT_1:171</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">s</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> &amp; <font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E6:41_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E7:41_1"/>
<font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="funct_4.html#T21" title="FUNCT_4:th.21">FUNCT_4:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>)</span><br/>

<a NAME="E8:41_1"/>
<span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:41_1"/>
<span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">s</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<a NAME="E2:41"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E3:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <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"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:41"/>
<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">d</font> <a href="extpro_1.html#R2" title="EXTPRO_1:pred.2">computes</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font></span><br/>

<a NAME="E5:41"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> st <br/>(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="extpro_1.html#K7" title="EXTPRO_1:func.7">Result</a> (<font color="Maroon" title="c3">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b1">s</font></span>)</span>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="extpro_1.html#D14" target="_self" title="EXTPRO_1:def.14">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:41"/>
<font color="Maroon" title="c4">d</font> is    <a href="extpro_1.html#M1" title="EXTPRO_1:mode.1">Autonomy</a> of <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T21" title="FUNCT_4:th.21">FUNCT_4:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
