Na=V1c0Ia<=c1V0Aa<c1V1F
precondition
Na=V1c0Ia=amodV0V1c0Ia<=c1V0Aa<c1V1F
a<c1ap
a<=c1an
a=amodanapc0
a<=c0an
variant decrease
a<adan
a<adanAa<=c0an
a<V2V0Aa<=c0V0LadivV0V1Ia=amodV0V1c0Ia<=c1V0Aa<c1V1F
a<c1V1LadivV0V1Ia=amodV0V1c0Ia<=c1V0Aa<c1V1F
a<=c1V2Ia<c1V1LadivV0V1Ia=amodV0V1c0Ia<=c1V0Aa<c1V1F
a<=c0V2Iia=V2c0a=V2a+V3c1AadividesapowerV1V3adivV0V1Aa<=c0V3Ea=amodV0V1c0FIa<=c1V0Aa<c1V1F
postcondition
a<=c0ar
adividesapoweraparadivanap
a=aresulta+arc1
a<=c0aresult
adividesapoweraparesultan
Na=amodanapc0
a=aresultc0
adividesapowerV1V2V0Ia<=c0V2Iia=V2c0a=V2a+V3c1AadividesapowerV1V3adivV0V1Aa<=c0V3Ea=amodV0V1c0FIa<=c1V0Aa<c1V1F
adividesapowerV1V2V0Aa<=c0V2Iia=V2c0a=V2a+V3c1AadividesapowerV1V3adivV0V1Aa<=c0V3Ea=amodV0V1c0FAa<=c1V4Aa<c1V1Aa<V4V0Aa<=c0V0LadivV0V1ANa=V1c0Ia=amodV0V1c0ANa=V1c0Ia<=c1V0Aa<c1V1F
VC for valuation
ia=avaluationV0V1c0a=avaluationV0V1a+avaluationadivV0V1V1c1a=amodV0V1c0Ia<=c1V0Ia<c1V1F
adividesapowerV3avaluationV2V3V2Aa<=c0avaluationV2V3Ia<=c1V2Ia<c1V3F
a=amoda*anapapc0
empty_shape
a=adiva*anapapan
a=avaluationa*anapapa+c1avaluationanap
a=avaluationa*V4V5V5a+c1avaluationV4V5ItOtOa=adiva*V4V5V5V4Aa=amoda*V4V5V5c0Ia<c1V5Ia<=c1V4F
a<=c1ab
a<=c0ae
a<=aec0
a<=c1apowerabae
base case
a<c0ae
a<=c1apowerabV6Ia<=c0V6Ia<=c1abIa<V6aeF
recursive case
a<=c1apowerV6V7Ia<=c0V7Ia<=c1V6F
a<=c0ak
a>akc0
a<a-akc1akAa<=c0ak
a<=c0a-akc1Aa<c1apAa<=c1an
a=avaluationa*anapowerapa-akc1apa+a-akc1avaluationanap
a=avaluationa*anapowerapakapavaluationa*a*anapowerapa-akc1apap
assertion
a=avaluationa*a*anapowerapa-akc1apapa+c1avaluationa*anapowerapa-akc1ap
a=avaluationa*anapowerapakapa+c1avaluationa*anapowerapa-akc1ap
VC for valuation_times_pow
a=avaluationa*anapowerapakapa+c1avaluationa*anapowerapa-akc1apItOa=avaluationa*a*anapowerapa-akc1apapa+c1avaluationa*anapowerapa-akc1apAa=avaluationa*anapowerapakapavaluationa*a*anapowerapa-akc1apap
a=avaluationa*anapowerapakapa+c1avaluationa*anapowerapa-akc1apAa=avaluationa*anapowerapV8apa+V8avaluationanapLa-akc1ONa>akc0
a=avaluationa*anapowerapakapa+akavaluationanap
a=avaluationa*V8apowerV9V10V9a+V10avaluationV8V9Ia=avaluationa*V8apowerV9V10V9a+c1avaluationa*V8apowerV9a-V10c1V9ItOa=avaluationa*a*V8apowerV9a-V10c1V9V9a+c1avaluationa*V8apowerV9a-V10c1V9Aa=avaluationa*V8apowerV9V10V9avaluationa*a*V8apowerV9a-V10c1V9V9Aa=avaluationa*V8apowerV9V11V9a+V11avaluationV8V9La-V10c1ONa>V10c0Aa=avaluationa*V8apowerV9V10V9a+c1avaluationa*V8apowerV9a-V10c1V9ItOa=avaluationa*a*V8apowerV9a-V10c1V9V9a+c1avaluationa*V8apowerV9a-V10c1V9Aa=avaluationa*V8apowerV9V10V9avaluationa*a*V8apowerV9a-V10c1V9V9Ia=avaluationa*V8apowerV9V12V9a+V12avaluationV8V9Aa<=c0V12Aa<c1V9Aa<=c1V8Aa<V12V10Aa<=c0V10La-V10c1Ia>V10c0Ia<=c0V10Aa<c1V9Aa<=c1V8F
a=avaluationa*V8apowerV9V10V9a+V10avaluationV8V9Ia<=c0V10Aa<c1V9Aa<=c1V8F
a=avaluationadivV11apowerV12V13V12c0LavaluationV11V12IaprimeV12Ia<=c1V11F
a<=c0av
adividesapowerapavan
Na=apowerapavc0
a=ana*aqapowerapav
a<=c0avAa<c1apAa<=c1aq
a=avaluationa*aqapowerapavapa+avavaluationaqap
a<=avavaluationanap
a<=V16avaluationV14V15Ia=avaluationa*V18apowerV15V16V15a+V16avaluationV18V15Aa<=c0V16Aa<c1V15Aa<=c1V18Aa=V14a*V18apowerV15V16LadivV14V17ANa=V17c0LapowerV15V16IadividesapowerV15V16V14Aa<=c0V16Aa<c1V15Aa<=c1V14F
VC for valuation_lower_bound
a<=V16avaluationV14V15IadividesapowerV15V16V14Ia<=c0V16Aa<c1V15Aa<=c1V14F
a<=akc0
a=avaluationapowerapakapak
a<c0ak
a=avaluationapowerapV17apV17Ia<=c0V17Ia<c1apIa<V17akF
a=avaluationapowerV17V18V17V18Ia<=c0V18Aa<c1V17F
Na=V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
Na=V21c0Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a<V22V19Aa<=c0V19Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a<c1V21Aa<=c1V20Aa<=c1V22Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=a*V19V20a*V23V21La*V22V20Ia=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
VC for valuation_monotonous
a=avaluationa*V19V20V21avaluationa*V23V21V21Ia=a*V19V20a*V23V21La*V22V20Ia=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=avaluationa*V23V21V21a+c1avaluationV23V21Ia=a*V19V20a*V23V21La*V22V20Ia=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=avaluationa*V19V20V21a+c1avaluationV23V21Ia=avaluationa*V23V21V21a+c1avaluationV23V21Aa=avaluationa*V19V20V21avaluationa*V23V21V21Aa=a*V19V20a*V23V21La*V22V20Ia=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a=avaluationa*V19V20V21a+c1avaluationV23V21ItOtOa=avaluationa*V23V21V21a+c1avaluationV23V21Aa=avaluationa*V19V20V21avaluationa*V23V21V21Aa=a*V19V20a*V23V21La*V22V20Ia=avaluationV19V21a+c1avaluationV22V21Ia<=avaluationV22V21avaluationa*V22V20V21Ia=V19a*V21V22LadivV19V21Ia=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a<=avaluationV19V21avaluationa*V19V20V21Ia=avaluationa*V19V20V21a+c1avaluationV23V21La*V22V20Aa=avaluationV19V21a+c1avaluationV22V21Aa<=avaluationV22V21avaluationa*V22V20V21Aa=V19a*V21V22LadivV19V21ONa=amodV19V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a<=avaluationV19V21avaluationa*V19V20V21Ia=avaluationa*V19V20V21a+c1avaluationV23V21ItOtOa=avaluationa*V23V21V21a+c1avaluationV23V21Aa=avaluationa*V19V20V21avaluationa*V23V21V21Aa=a*V19V20a*V23V21La*V22V20Aa=avaluationV19V21a+c1avaluationV22V21Aa<=avaluationV22V21avaluationa*V22V20V21Aa=V19a*V21V22LadivV19V21ONa=amodV19V21c0Aa=avaluationa*V19V20V21a+c1avaluationV25V21ItOtOa=avaluationa*V25V21V21a+c1avaluationV25V21Aa=avaluationa*V19V20V21avaluationa*V25V21V21Aa=a*V19V20a*V25V21La*V24V20Ia=avaluationV19V21a+c1avaluationV24V21Aa=avaluationV19V21a+c1avaluationV24V21Ia<=avaluationV24V21avaluationa*V24V20V21Aa<c1V21Aa<=c1V20Aa<=c1V24Aa<V24V19Aa<=c0V19Ia=V19a*V21V24Aa=V19a*V21V24LadivV19V21ANa=V21c0Ia=amodV19V21c0ANa=V21c0Ia<c1V21Aa<=c1V20Aa<=c1V19F
a<=avaluationV19V21avaluationa*V19V20V21Ia<c1V21Aa<=c1V20Aa<=c1V19F
NadividesV23V22qa=avaluationV22V23c0Ia<c1V23Ia<=c1V22F
a=avaluationa*V24V25V26c0Ia=avaluationV25V26c0Ia=avaluationV24V26c0IaprimeV26Ia<=c1V25Ia<=c1V24F
a<=c1ac
aprimeap
a=avaluationacapc0
Na=apc0
a<=c1acAa<=c1ad
a=avaluationa*adacapavaluationadap
a=avaluationa*anacapavaluationa*a*adacapap
a<=c1a*adac
apply premises
tOtOa=adiva*a*adacapapa*adacAa=amoda*a*adacapapc0
a=avaluationa*a*adacapapa+c1avaluationa*adacap
a=a+c1avaluationa*adacapa+c1avaluationadap
a=a+c1avaluationadapavaluationanap
a=a+c1avaluationadapavaluationanapAa=a+c1avaluationa*adacapa+c1avaluationadapAa=avaluationa*a*adacapapa+c1avaluationa*adacapAa=avaluationa*anacapavaluationa*a*adacapap
a=a+c1avaluationV27apavaluationanapAa=a+c1avaluationa*V27acapa+c1avaluationV27apAa=avaluationa*a*V27acapapa+c1avaluationa*V27acapAa=avaluationa*anacapavaluationa*a*V27acapapAa=avaluationa*V27acapavaluationV27apLadivanapONa=amodanapc0
a=avaluationa*anacapavaluationanap
a=avaluationa*V27V28V29avaluationV27V29Ia=a+c1avaluationV30V29avaluationV27V29Aa=a+c1avaluationa*V30V28V29a+c1avaluationV30V29Aa=avaluationa*a*V30V28V29V29a+c1avaluationa*V30V28V29Aa=avaluationa*V27V28V29avaluationa*a*V30V28V29V29Aa=avaluationa*V30V28V29avaluationV30V29LadivV27V29ONa=amodV27V29c0Aa=a+c1avaluationV31V29avaluationV27V29Aa=a+c1avaluationa*V31V28V29a+c1avaluationV31V29Aa=avaluationa*a*V31V28V29V29a+c1avaluationa*V31V28V29Aa=avaluationa*V27V28V29avaluationa*a*V31V28V29V29Ia=avaluationa*V31V28V29avaluationV31V29Aa=avaluationV28V29c0AaprimeV29Aa<=c1V28Aa<=c1V31Aa<V31V27Aa<=c0V27LadivV27V29ANa=V29c0Ia=amodV27V29c0ANa=V29c0Ia=avaluationV28V29c0AaprimeV29Aa<=c1V28Aa<=c1V27F
VC for valuation_times_nondiv
a=avaluationa*V27V28V29avaluationV27V29Ia=avaluationV28V29c0IaprimeV29Ia<=c1V28Aa<=c1V27F
a<=c1an1
a<=c1an2
a=an1a*apowerapav1ac1
a=an2a*apowerapav2ac2
a=avaluationac1apc0
a=avaluationac2apc0
a<=c1ac1
a<=c1ac2
a=avaluationa*ac1ac2apc0
a=a*an1an2a*a*apowerapav1apowerapav2a*ac1ac2
a=a*apowerapa+av1av2a*ac1ac2a*apowerapa+av1av2a*ac1ac2
a<=c0av1
rewrite premises
a<=c0av2
a=a*a*apowerapav1apowerapav2a*ac1ac2a*apowerapa+av1av2a*ac1ac2
a=avaluationa*an1an2apavaluationa*apowacap
a<=c1apow
a<=c1acAa<=c1apow
a=avaluationa*apowacapavaluationapowap
a=avaluationapowapa+av1av2
a=an1a*apowerapV30V32Ladivan2apowerapV31Ladivan1apowerapV30Lavaluationan2apLavaluationan1ap
a=an2a*apowerapV35V37Ladivan2apowerapV35Ladivan1apowerapV34Lavaluationan2apLavaluationan1ap
a=avaluationV40apc0Ladivan2apowerapV39Ladivan1apowerapV38Lavaluationan2apLavaluationan1ap
a=avaluationV45apc0Ladivan2apowerapV43Ladivan1apowerapV42Lavaluationan2apLavaluationan1ap
a=avaluationa*V48V49apc0Ladivan2apowerapV47Ladivan1apowerapV46Lavaluationan2apLavaluationan1ap
a=a*an1an2a*a*apowerapV50apowerapV51a*V52V53Ladivan2apowerapV51Ladivan1apowerapV50Lavaluationan2apLavaluationan1ap
a=a*a*apowerapV54apowerapV55a*V56V57a*apowerapa+V54V55a*V56V57Ladivan2apowerapV55Ladivan1apowerapV54Lavaluationan2apLavaluationan1ap
a<=c1V60La*V60V61Lapowerapa+V58V59Ladivan2apowerapV59Ladivan1apowerapV58Lavaluationan2apLavaluationan1ap
a<=c1V67La*V66V67Lapowerapa+V64V65Ladivan2apowerapV65Ladivan1apowerapV64Lavaluationan2apLavaluationan1ap
a<=c1V75La*V72V73Lapowerapa+V70V71Ladivan2apowerapV71Ladivan1apowerapV70Lavaluationan2apLavaluationan1ap
a=avaluationa*an1an2apavaluationa*V80V81apLa*V78V79Lapowerapa+V76V77Ladivan2apowerapV77Ladivan1apowerapV76Lavaluationan2apLavaluationan1ap
a=avaluationa*V86V87apavaluationV86apLa*V84V85Lapowerapa+V82V83Ladivan2apowerapV83Ladivan1apowerapV82Lavaluationan2apLavaluationan1ap
a=avaluationV92apa+V88V89La*V90V91Lapowerapa+V88V89Ladivan2apowerapV89Ladivan1apowerapV88Lavaluationan2apLavaluationan1ap
a=avaluationa*an1an2apa+avaluationan1apavaluationan2ap
a=avaluationa*V30V31V32a+avaluationV30V32avaluationV31V32ItOtOtOtOtOtOtOtOtOtOa=avaluationV37V32a+V33V34Aa=avaluationa*V37V38V32avaluationV37V32Aa=avaluationa*V30V31V32avaluationa*V37V38V32Aa<=c1V38Aa<=c1V36Aa<=c1V35La*V35V36LapowerV32a+V33V34Aa=a*a*apowerV32V33apowerV32V34a*V35V36a*apowerV32a+V33V34a*V35V36Aa=a*V30V31a*a*apowerV32V33apowerV32V34a*V35V36Aa=avaluationa*V35V36V32c0Aa=avaluationV36V32c0Aa=avaluationV35V32c0Aa=V31a*apowerV32V34V36Aa=V30a*apowerV32V33V35LadivV31apowerV32V34LadivV30apowerV32V33LavaluationV31V32LavaluationV30V32IaprimeV32Ia<=c1V31Ia<=c1V30F
a>avaluationV39V40c0qa=amodV39V40c0Ia<c1V40Ia<=c1V39F
adividesapowerapavaluationanapan
a=ana*apowerapavaluationanapadivanapowerapavaluationanap
a=V41a*apowerV42avaluationV41V42adivV41apowerV42avaluationV41V42ItOadividesapowerV42avaluationV41V42V41Ia<c1V42Ia<=c1V41F

342704f66c6fbb40672670eb51c19961 24H23
0562620960b829a9b21270fdb1756ae2 1H0
f67fd9516f93d022cd4f4a6ac6c0974b 1H2
1a752cba52ac56cc8bbd86c4bd6d979d 7H10
2ebc0144c0e41f4bf03fd6840bf602f0 7H9H5H4H3
04e091483e3caa1d8c8ebe45149e3d92 7H6H5H4H3
603630690e0ad7c8036bd9c491faab06 7H8H5H4H3
f3e859eb5475f4fb219cc786eb881476 1H11
8722eaa7eaeba23383cbe836ab216694 1H12
54bd8bfb7c43a23b4220634b32312371 14H13
4f136f8183ea21e47e75b8b4b55c317f 14H22
53b1239e6c13fe83ea70eaac5c6a3a5b 14H19H18H17H16H15H5H4H3
e404acb2b4ca127dd3392d654bd5fd60 14H19H18H21H20H4H3
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77263fa1330ede7daeb11e75d9cc9445 28H27H3H4H26H25
8bf0d45d9ef3cde2d8da7dc77a75f8bb 28H29H27H3H4H26H25
346efa4c32e6a0c568e33cd62b03b60e 28H30H29H27H3H4H26H25
7de74e172e743222747ae0c6b9a54fb0 28H40H31H26H25
dca30f1733c19456f29b03d34323d557 28H35H33H32H31H26H25
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4c5eeca95c8ef952fbe8931316437358 50H54H40H31H26H25
c623023466dd91754aa0797d4871f2b1 7H43H42H41H3H4H40H31H26H25
139f3d405811a43ad62ed23162c0f340 1H44H42H41H3H4H40H31H26H25
faa5d189d4075a6c270c6f97a717b911 47H51H45H42H41H3H4H40H31H26H25
4c454e11130f6e6e42a4d7b779596179 47H46H45H42H41H3H4H40H31H26H25
5f37351aeb180f9f7b4e26c745506c1c 47H48H45H42H41H3H4H40H31H26H25
a388579e737c0d549f732d65f922c3bf 50H49H48H46H45H42H41H3H4H40H31H26H25
c8e1a15414cc39ae7a426b7256040ece 14H53H52H41H3H4H40H31H26H25
1aabd3e556b2876240b136d01eddd12b 28H56H55H40H31H26H25
51267a14ff6919725abbf1a3faa49fe0 65H64H56H55H40H31H26H25
c5aba5572590d32a2478a5d091b52cb5 1H59H58H57H3H4H56H55H40H31H26H25
df21f62537a7f0df9d76bf77afed7249 47H60H58H57H3H4H56H55H40H31H26H25
8d4acf5523915b1c51e9f1a0f96a5cdb 1H61H60H58H57H3H4H56H55H40H31H26H25
3e53125c293a8ad2a73cc98fa0560b1d 14H63H62H60H58H57H3H4H56H55H40H31H26H25
ee59fbe6f2b6d81ac7e1bdd8d6969746 28H71H66H56H55H40H31H26H25
11fd61f699277b3cdacabc96e65b5245 28H68H41H3H66H56H55H40H31H26H25
442d6f2ac9544ce2e4fd7b964e96b033 36H68H67H41H3H66H56H55H40H31H26H25
2520245f332948b2709bab13a1c10595 39H68H70H69H41H3H66H56H55H40H31H26H25
9a3124107093e607ceceb7405712a9fe 79H85H71H66H56H55H40H31H26H25
186490c6447b0e617c487ee5d8f93595 1H72H71H66H56H55H40H31H26H25
4599519530733459077371e1a0e520fc 1H73H71H66H56H55H40H31H26H25
45159bf1899a9fc3d51c63d89225b2e5 47H74H71H66H56H55H40H31H26H25
f13fc51cfc8b5156bfd0ea1dbbfb287e 7H75H71H66H56H55H40H31H26H25
c6a37e012cd8e337cca86ff40e3fb5b5 1H76H71H66H56H55H40H31H26H25
2850338eeaaddceead11cfcfc7dc8db8 47H77H71H66H56H55H40H31H26H25
8674f845d08ee093e6993a0ae2e72833 47H83H71H66H56H55H40H31H26H25
74b0b852a8d1cd0efe444a139c394bf6 79H78H71H66H56H55H40H31H26H25
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