colsort-dirtyboundhalf#r mx0 = #r mx, #c mx0 = #c mx, #c mx ≠ 0
⊦ colsorted(mx0, #c mx, mx) ∧ mx0.dirtyrows≤(bound) ∧ srowsorted(mx0, #r mx0, mx0) → mx.dirtyrows≤(bound /↑ 2)colsorted-defcountodd-maxcol0-boundedcountevn-maxcol0-boundedclean0rows-boundedcount-add-even-odd-indmax0column-countcoldivup-defmax0column-determines-clean1rowsmax0column-clean0rowsboundedexists-max0columndirtyrows-defdirtyrowsbound-def
2964colsort-dirtyboundhalf-proofcolsort-dirtyboundhalf-proof-infols
The proof is valid.ls
pshearsort-correct
../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/eq/longlemmainfo.xmleq../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/le-addex/longlemmainfo.xmlle-addex../../../../../../lib/basic/specs/nat-even/export/unit.xmlnat-even../../../../../../lib/basic/specs/nat-even/export/Min-left/longlemmainfo.xmlMin-left../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/f/longlemmainfo.xmlf../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/le-def/longlemmainfo.xmlle-def../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/lf-01/longlemmainfo.xmllf-01../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ls-le-simp/longlemmainfo.xmlls-le-simp../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ge/longlemmainfo.xmlge../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/refl-nat/longlemmainfo.xmlrefl-nat../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ler/longlemmainfo.xmller../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/c/longlemmainfo.xmlc../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/a/longlemmainfo.xmla../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/eqs/longlemmainfo.xmleqs../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/fle/longlemmainfo.xmlfle../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/mult-c/longlemmainfo.xmlmult-c../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/mult-a/longlemmainfo.xmlmult-a../../../../../../lib/basic/specs/nat-div/export/unit.xmlnat-div../../../../../../lib/basic/specs/nat-div/export/two-mdiv2-02/longlemmainfo.xmltwo-mdiv2-02../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/le-num/longlemmainfo.xmlle-num../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/anti/longlemmainfo.xmlanti../../../../../../lib/basic/specs/nat-div/export/unit.xmlnat-div../../../../../../lib/basic/specs/nat-div/export/le-div-to-mult/longlemmainfo.xmlle-div-to-mult../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lels/longlemmainfo.xmllels../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/s-04/longlemmainfo.xmls-04../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/l/longlemmainfo.xmll../../../../../../lib/basic/specs/nat-div/export/unit.xmlnat-div../../../../../../lib/basic/specs/nat-div/export/ls-02/longlemmainfo.xmlls-02../../../../../../lib/basic/specs/nat-div/export/unit.xmlnat-div../../../../../../lib/basic/specs/nat-div/export/two-zero-01-01/longlemmainfo.xmltwo-zero-01-01../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/le-ls-simp/longlemmainfo.xmlle-ls-simp../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/fle-01/longlemmainfo.xmlfle-01../../../../../../lib/basic/specs/nat-div/export/unit.xmlnat-div../../../../../../lib/basic/specs/nat-div/export/div-elim/longlemmainfo.xmldiv-elim../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/lf-02/longlemmainfo.xmllf-02../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lels-02/longlemmainfo.xmllels-02../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/l-num-05/longlemmainfo.xmll-num-05../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/one-01/longlemmainfo.xmlone-01../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/succ/longlemmainfo.xmlsucc../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/add-base/longlemmainfo.xmladd-base../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/two-succ-05/longlemmainfo.xmltwo-succ-05../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/let/longlemmainfo.xmllet../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/l-02/longlemmainfo.xmll-02../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/zero-02/longlemmainfo.xmlzero-02../../../../../../lib/basic/specs/nat-mult/export/unit.xmlnat-mult../../../../../../lib/basic/specs/nat-mult/export/two-ls-01/longlemmainfo.xmltwo-ls-01../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/lf/longlemmainfo.xmllf../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/trans-nat/longlemmainfo.xmltrans-nat../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/l-05/longlemmainfo.xmll-05../../../../../../lib/polybasic/specs/matrix+array/export/unit.xmlmatrix+array../../../../../../lib/polybasic/specs/matrix+array/export/selcol-size/longlemmainfo.xmlselcol-size../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/eq-01/longlemmainfo.xmleq-01../../../../../../lib/basic/specs/nat-even/export/unit.xmlnat-even../../../../../../lib/basic/specs/nat-even/export/Min-right/longlemmainfo.xmlMin-right../../../../../../lib/basic/specs/nat-even/export/unit.xmlnat-even../../../../../../lib/basic/specs/nat-even/export/min-a/longlemmainfo.xmlmin-a../../../../../../lib/basic/specs/nat-even/export/unit.xmlnat-even../../../../../../lib/basic/specs/nat-even/export/min-c/longlemmainfo.xmlmin-c