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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="msafree2.html#V4" title="MSAFREE2:attr.4">locally-finite</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">V</font> being   <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">X</font> being   <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b2">V</font><br/> for <font color="Olive" title="b4">G</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b5">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b4">G</font>  st <font color="Olive" title="b5">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b3">X</font>,<font color="Olive" title="b1">A</font> holds <br/>for <font color="Olive" title="b6">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Olive" title="b3">X</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b5">C</font><br/> for <font color="Olive" title="b7">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b2">V</font>  st <font color="Olive" title="b7">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b3">X</font> holds <br/>for <font color="Olive" title="b8">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b5">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b8">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b7">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">t</font> &amp; ( for <font color="Olive" title="b9">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Olive" title="b3">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Olive" title="b1">A</font></span>)</span>  st <font color="Olive" title="b9">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b6">f</font> holds <br/>for <font color="Olive" title="b10">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b9">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b8">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b7">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b10">h</font>,<font color="Olive" title="b1">A</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="msafree2.html#V4" title="MSAFREE2:attr.4">locally-finite</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being   <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">X</font> being   <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b3">G</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b4">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b3">G</font>  st <font color="Olive" title="b4">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c2">A</font> holds <br/>for <font color="Olive" title="b5">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b4">C</font><br/> for <font color="Olive" title="b6">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">V</font>  st <font color="Olive" title="b6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b2">X</font> holds <br/>for <font color="Olive" title="b7">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b4">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b7">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b6">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">t</font> &amp; ( for <font color="Olive" title="b8">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b8">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b5">f</font> holds <br/>for <font color="Olive" title="b9">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b8">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b7">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b6">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b9">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">V</font> be    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font><br/> for <font color="Olive" title="b2">G</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b3">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b2">G</font>  st <font color="Olive" title="b3">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">A</font> holds <br/>for <font color="Olive" title="b4">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b3">C</font><br/> for <font color="Olive" title="b5">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Olive" title="b1">X</font> holds <br/>for <font color="Olive" title="b6">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b6">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b5">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t</font> &amp; ( for <font color="Olive" title="b7">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b7">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font> holds <br/>for <font color="Olive" title="b8">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b7">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b6">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b5">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b8">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/><b>let </b><font color="Maroon" title="c4">X</font> be    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b2">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b2">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b2">C</font><br/> for <font color="Olive" title="b4">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/>for <font color="Olive" title="b5">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b5">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">t</font> &amp; ( for <font color="Olive" title="b6">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b6">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b3">f</font> holds <br/>for <font color="Olive" title="b7">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b6">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b5">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b4">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b7">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c5">G</font>  st <font color="Olive" title="b1">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> holds <br/>for <font color="Olive" title="b2">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">C</font><br/> for <font color="Olive" title="b3">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/>for <font color="Olive" title="b4">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b4">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">t</font> &amp; ( for <font color="Olive" title="b5">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b5">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">f</font> holds <br/>for <font color="Olive" title="b6">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b5">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b4">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b6">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/><b>let </b><font color="Maroon" title="c6">C</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c5">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font> implies for <font color="Olive" title="b1">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/>for <font color="Olive" title="b3">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">t</font> &amp; ( for <font color="Olive" title="b4">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b4">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f</font> holds <br/>for <font color="Olive" title="b5">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b4">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b5">h</font>,<font color="Maroon" title="c2">A</font> ) ) )</span><br/>











<b>assume </b><a NAME="E1:87"/><i><font color="Green" title="E59">A1</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="circtrm1.html#R7" title="CIRCTRM1:pred.7">calculates</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/>for <font color="Olive" title="b3">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">t</font> &amp; ( for <font color="Olive" title="b4">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b4">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">f</font> holds <br/>for <font color="Olive" title="b5">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b4">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b3">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b5">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/>

<b>let </b><font color="Maroon" title="c7">f</font> be    <a href="circtrm1.html#M2" title="CIRCTRM1:mode.2">SortMap</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>  st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> &amp; ( for <font color="Olive" title="b3">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b3">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> holds <br/>for <font color="Olive" title="b4">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b3">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b2">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b4">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/>

<b>consider </b><font color="Maroon" title="c8">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:87"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font> <a href="circtrm1.html#R4" title="CIRCTRM1:pred.4">form_embedding_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c6">C</font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E1:87"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="circtrm1.html#D17" target="_self" title="CIRCTRM1:def.17">Def17</a></i>;<br/>
<a NAME="E4:87"/><i><font color="Green" title="E61">A3</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="circtrm1.html#R3" title="CIRCTRM1:pred.3">preserves_inputs_of</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font>
 
<b>by </b><i><a class="txt" href="circtrm1.html#E1:87"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="circtrm1.html#D17" target="_self" title="CIRCTRM1:def.17">Def17</a></i>;<br/>
<a NAME="E5:87"/><i><font color="Green" title="E62">A4</font></i>: 
<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> ,<font color="Maroon" title="c5">G</font>
 
<b>by </b><i><a class="txt" href="circtrm1.html#E3:87"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="circtrm1.html#D12" target="_self" title="CIRCTRM1:def.12">Def12</a></i>;<br/>
<b>let </b><font color="Maroon" title="c9">t</font> be   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font> implies for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font> &amp; ( for <font color="Olive" title="b2">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b2">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> holds <br/>for <font color="Olive" title="b3">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b2">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b3">h</font>,<font color="Maroon" title="c2">A</font> ) ) )</span><br/>

<b>assume </b><a NAME="E6:87"/><i><font color="Green" title="E63">A5</font></i>: 
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_9.html#K9" title="TREES_9:func.9">Subtrees</a> <font color="Maroon" title="c4">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font> holds <br/> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font> &amp; ( for <font color="Olive" title="b2">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b2">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> holds <br/>for <font color="Olive" title="b3">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b2">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b3">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/>

<b>let </b><font color="Maroon" title="c10">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font> &amp; ( for <font color="Olive" title="b1">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b1">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> holds <br/>for <font color="Olive" title="b2">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b1">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b2">h</font>,<font color="Maroon" title="c2">A</font> ) )</span><br/>

<b>reconsider </b><font color="Maroon" title="c11">s'</font> = <font color="Maroon" title="c10">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span> <b>by </b><i><a class="txt" href="circtrm1.html#E3:87"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="circtrm1.html#T45" target="_self" title="CIRCTRM1:th.45">Th45</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">t'</font> = <font color="Maroon" title="c9">t</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span> <b>by </b><i><a class="txt" href="circtrm1.html#E6:87"><i><font color="Green" title="E63">A5</font></i></a></i>;<br/>
<a NAME="E9:87"/><i><font color="Green" title="E64">A6</font></i>: 
(  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c11">s'</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c12">t'</font> &amp;  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c11">s'</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> )
 
<b>by </b><i><a class="txt" href="circtrm1.html#E3:87"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="circtrm1.html#E4:87"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="circtrm1.html#T22" target="_self" title="CIRCTRM1:th.22">Th22</a>, <a class="ref" href="circtrm1.html#T48" target="_self" title="CIRCTRM1:th.48">Th48</a></i>;<br/>
<b>hence </b><a NAME="E10:87"/>
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p3">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span> <a href="facirc_1.html#R1" title="FACIRC_1:pred.1">is_stable_at</a> <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E3:87"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="circtrm1.html#E4:87"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="circtrm1.html#T50" target="_self" title="CIRCTRM1:th.50">Th50</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s'</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b1">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> holds <br/>for <font color="Olive" title="b2">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Olive" title="b1">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b2">h</font>,<font color="Maroon" title="c2">A</font></span><br/>

<b>let </b><font color="Maroon" title="c13">s'</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K6" title="CIRCTRM1:func.6">-Circuit</a> <font color="Maroon" title="c2">A</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c13">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font> implies for <font color="Olive" title="b1">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Maroon" title="c13">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">A</font> )</span><br/>

<b>assume </b><a NAME="E11:87"/><i><font color="Green" title="E65">A7</font></i>: 
<font color="Maroon" title="c13">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being   <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Maroon" title="c13">s'</font> holds  <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">A</font></span><br/>

<b>let </b><font color="Maroon" title="c14">h</font> be    <a href="circtrm1.html#M1" title="CIRCTRM1:mode.1">CompatibleValuation</a> of <font color="Maroon" title="c13">s'</font>; <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"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Maroon" title="c14">h</font>,<font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E12:87"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">f</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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s'</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">t'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Maroon" title="c14">h</font>,<font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="txt" href="circtrm1.html#E5:87"><i><font color="Green" title="E62">A4</font></i></a>, <a class="ref" href="circtrm1.html#T22" target="_self" title="CIRCTRM1:th.22">Th22</a>, <a class="ref" href="pua2mss1.html#D13" title="PUA2MSS1:def.13">PUA2MSS1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E13:87"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s</font>,<span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="trees_1.html#K6" title="TREES_1:func.6">height</a> <span class="p4">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">t</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="circtrm1.html#K7" title="CIRCTRM1:func.7">@</a> <font color="Maroon" title="c14">h</font>,<font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E9:87"><i><font color="Green" title="E64">A6</font></i></a>, <a class="txt" href="circtrm1.html#E11:87"><i><font color="Green" title="E65">A7</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</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>
