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xpos)</SEQ></GOALSEQ></SEQGOAL></LEMMAGOAL><LEMMATYPE><USERLEMMA/></LEMMATYPE><USEDLEMMAS><LIST><LE>leftneighbor</LE><LE>leftneighbor-succ</LE><LE>leftneighbor-rec</LE><LE>leftneighbor-zero</LE><LE>leftneighbor-base</LE><LE>leftneighbor-h-le</LE><LE>valid-stack-leftneighbor-succ-gen</LE><LE>one-based-lookup</LE><LE>first-lower-rec</LE></LIST></USEDLEMMAS><SMTINFOS><LIST></LIST></SMTINFOS><MAINGOALS><LIST></LIST></MAINGOALS><USERACTIONS>6</USERACTIONS><PROOFSTEPS>15</PROOFSTEPS><PROVEDP><T/></PROVEDP><PROOFEXISTSP><T/></PROOFEXISTSP><PROOFFILENAME>valid-stack-leftneighbor-succ-proof</PROOFFILENAME><LEMMAPROOFBAG><NONE/></LEMMAPROOFBAG><SAVETREEP><F/></SAVETREEP><INFOFILENAME>valid-stack-leftneighbor-succ-proof-info</INFOFILENAME><LEMMAPROOFINFOBAG><NONE/></LEMMAPROOFINFOBAG><SAVEINFOSP><F/></SAVEINFOSP><SIMPFEATURES><LIST></LIST></SIMPFEATURES><HISTINFO><LIST></LIST></HISTINFO></LEMMAINFO><VALIDITY>The proof is valid.</VALIDITY><FEATURES><LIST></LIST></FEATURES><HISTORY><LIST></LIST></HISTORY><USEDBY><LIST><LE>LEFTNEIGHBORS-correct</LE></LIST></USEDBY><USEDBYUNITS><LIST></LIST></USEDBYUNITS><COMMENT></COMMENT><USED_SPECLEMS></USED_SPECLEMS><USED_SIMPRULES><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-data/export/unit.xml</HTMLTARGET><HTMLSTRING>list-data</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-data/export/l/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>l</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat-basic/export/unit.xml</HTMLTARGET><HTMLSTRING>nat-basic</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat-basic/export/f/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>f</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/unit.xml</HTMLTARGET><HTMLSTRING>list</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME>natlist</INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/a/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>a</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/unit.xml</HTMLTARGET><HTMLSTRING>nat</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/pred-03/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>pred-03</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/unit.xml</HTMLTARGET><HTMLSTRING>list</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME>natlist</INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/e-01/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>e-01</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/unit.xml</HTMLTARGET><HTMLSTRING>list</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME>natlist</INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list/export/c-08/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>c-08</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/unit.xml</HTMLTARGET><HTMLSTRING>nat</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/ler/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>ler</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/oelem/export/unit.xml</HTMLTARGET><HTMLSTRING>oelem</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME>natlist</INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/oelem/export/lel/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>lel</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/unit.xml</HTMLTARGET><HTMLSTRING>nat</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/fle-01/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>fle-01</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/unit.xml</HTMLTARGET><HTMLSTRING>nat</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat/export/le-def/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>le-def</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-del/export/unit.xml</HTMLTARGET><HTMLSTRING>list-del</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-del/export/get-zero/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>get-zero</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat-basic/export/unit.xml</HTMLTARGET><HTMLSTRING>nat-basic</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/nat-basic/export/zero/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>zero</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-data/export/unit.xml</HTMLTARGET><HTMLSTRING>list-data</HTMLSTRING></HTMLLINK></SPECNAME><INSTNAME></INSTNAME><LEMNAME><HTMLLINK><HTMLTARGET>../../../../../../lib/basic/specs/list-data/export/elim-1/longlemmainfo.xml</HTMLTARGET><HTMLSTRING>elim-1</HTMLSTRING></HTMLLINK></LEMNAME></USED_SEQ><USED_SEQ><SPECNAME><HTMLLINK><HTMLTARGET>../../../../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