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<span class="kw">let </span><font color="Maroon" title="c1">Q</font> be   <a href="quantal1.html#NM5" title="QUANTAL1:NM.5">Girard-Quantale</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Olive" title="b3">c</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">c</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Olive" title="b1">a</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</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="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c4">c</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span> )</span><br/>







<span class="kw">thus </span><font color="Maroon" title="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> = 
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T26" target="_self" title="QUANTAL1:th.26">Th26</a></span>
<br/>.= 
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T6" target="_self" title="QUANTAL1:th.6">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c4">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T26" target="_self" title="QUANTAL1:th.26">Th26</a></span>
; <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"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font> = 
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T26" target="_self" title="QUANTAL1:th.26">Th26</a></span>
<br/>.= 
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T6" target="_self" title="QUANTAL1:th.6">Th6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="quantal1.html#K9" title="QUANTAL1:func.9">delta</a> <font color="Maroon" title="c2">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quantal1.html#T26" target="_self" title="QUANTAL1:th.26">Th26</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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