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<span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="abcmiz_1.html#V3" title="ABCMIZ_1:attr.3">initialized</a>  <a href="abcmiz_1.html#NM5" title="ABCMIZ_1:NM.5">ConstructorSignature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T1</font>, <font color="Olive" title="b2">T2</font>, <font color="Olive" title="b3">T3</font> being   <a href="abcmiz_1.html#M3" title="ABCMIZ_1:mode.3">quasi-type</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">T1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Olive" title="b2">T2</font> &amp; <font color="Olive" title="b2">T2</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Olive" title="b3">T3</font> holds <br/><font color="Olive" title="b1">T1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Olive" title="b3">T3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">t1</font>, <font color="Maroon" title="c4">t2</font>, <font color="Maroon" title="c5">t3</font> be    <a href="abcmiz_1.html#M3" title="ABCMIZ_1:mode.3">quasi-type</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">t1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c4">t2</font> &amp; <font color="Maroon" title="c4">t2</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c5">t3</font> implies <font color="Maroon" title="c3">t1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c5">t3</font> )</span><br/>



<span class="kw">given </span><font color="Maroon" title="c6">f1</font> being   <a href="abcmiz_1.html#NM13" title="ABCMIZ_1:NM.13">valuation</a> of <font color="Maroon" title="c2">C</font><span class="kw"> such that </span><a NAME="E2:93"/><span class="lab"><font color="Green" title="E38">Z0</font></span>: 
( <span class="p1">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c6">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c3">t1</font> &amp; <span class="p1">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="abcmiz_1.html#K62" title="ABCMIZ_1:func.62">at</a> <font color="Maroon" title="c6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c3">t1</font> )
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="abcmiz_a.html#D23" target="_self" title="ABCMIZ_A:def.23">ABCMIZ_A:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">t2</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c5">t3</font> or <font color="Maroon" title="c3">t1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c5">t3</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c7">f2</font> being   <a href="abcmiz_1.html#NM13" title="ABCMIZ_1:NM.13">valuation</a> of <font color="Maroon" title="c2">C</font><span class="kw"> such that </span><a NAME="E4:93"/><span class="lab"><font color="Green" title="E39">Z1</font></span>: 
( <span class="p1">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c7">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c4">t2</font> &amp; <span class="p1">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K62" title="ABCMIZ_1:func.62">at</a> <font color="Maroon" title="c7">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c4">t2</font> )
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="abcmiz_a.html#D23" target="_self" title="ABCMIZ_A:def.23">ABCMIZ_A:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">t1</font> <a href="abcmiz_a.html#R3" title="ABCMIZ_A:pred.3">matches_with</a> <font color="Maroon" title="c5">t3</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c7">f2</font> <a href="abcmiz_1.html#K65" title="ABCMIZ_1:func.65">at</a> <font color="Maroon" title="c6">f1</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="abcmiz_a.html#D23" target="_self" title="ABCMIZ_A:def.23">ABCMIZ_A:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="abcmiz_1.html#K65" title="ABCMIZ_1:func.65">at</a> <font color="Maroon" title="c6">f1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c3">t1</font> &amp; <span class="p1">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K62" title="ABCMIZ_1:func.62">at</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="abcmiz_1.html#K65" title="ABCMIZ_1:func.65">at</a> <font color="Maroon" title="c6">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c3">t1</font> )</span><br/>

<a NAME="E5:93"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c6">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c6">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E39">Z1</font></span></a>, <a class="ref" href="abcmiz_1.html#T146" title="ABCMIZ_1:th.146">ABCMIZ_1:146</a></span>;<br/>
<a NAME="E6:93"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <font color="Maroon" title="c6">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c3">t1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E38">Z0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:93"/>
( <span class="p1">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K63" title="ABCMIZ_1:func.63">at</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="abcmiz_1.html#K65" title="ABCMIZ_1:func.65">at</a> <font color="Maroon" title="c6">f1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c3">t1</font> &amp; <span class="p1">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c5">t3</font></span>)</span> <a href="abcmiz_1.html#K62" title="ABCMIZ_1:func.62">at</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="abcmiz_1.html#K65" title="ABCMIZ_1:func.65">at</a> <font color="Maroon" title="c6">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c3">t1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E38">Z0</font></span></a>, <a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E39">Z1</font></span></a>, <a class="ref" href="abcmiz_1.html#T149" title="ABCMIZ_1:th.149">ABCMIZ_1:149</a>, <a class="ref" href="abcmiz_1.html#T150" title="ABCMIZ_1:th.150">ABCMIZ_1:150</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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