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<a NAME="E1:157_1_2"/>
 for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicBasicAsgn</a>)</span>)</span>  st (  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b3">a</font> ) &amp; (  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Olive" title="b2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b3">a</font> ) holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="157_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicBasicAsgn</a>)</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b1">a</font> ) &amp; (  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b1">a</font> ) implies <font color="Maroon" title="c1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:157_1_2_1"/><span class="lab"><font color="Green" title="E111">A3</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b1">a</font>
 <span class="kw">and </span><br/><a NAME="E2:157_1_2_1"/><span class="lab"><font color="Green" title="E112">A4</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b1">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f2</font></span><br/>

<a NAME="E3:157_1_2_1"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="157_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  implies <font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:157_1_2_1_1"/><span class="lab"><font color="Green" title="E113">A5</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font></span><br/>

<a NAME="E2:157_1_2_1_1"/>
<font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:157_1_2_1"><span class="lab"><font color="Green" title="E111">A3</font></span></a>, <a class="txt" href="#E1:157_1_2_1_1"><span class="lab"><font color="Green" title="E113">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:157_1_2_1_1"/>
<font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:157_1_2_1"><span class="lab"><font color="Green" title="E112">A4</font></span></a>, <a class="txt" href="#E1:157_1_2_1_1"><span class="lab"><font color="Green" title="E113">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<span class="kw">hence </span><a NAME="E4:157_1_2_1"/>
<font color="Maroon" title="c1">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T12" onmouseover="rs('funct_2/T12')" onmouseout="rh()">FUNCT_2:12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<span class="kw">hence </span><a NAME="E2:157_1_2"/>
 for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <span class="p1">(<span class="default"><a href="modelc_2.html#K42" title="MODELC_2:func.42">Inf_seqModel</a> (<a href="modelc_2.html#K43" title="MODELC_2:func.43">AtomicFamily</a>,<a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicBasicAsgn</a>)</span>)</span>  st (  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b3">a</font> ) &amp; (  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>  holds <br/><font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K45" title="MODELC_2:func.45">AtomicAsgn</a> <font color="Olive" title="b3">a</font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
