a<=c0V0E
VC for array
a<=c0alengthV0FalengthV0
a=aeltsaV1V2V3asetaeltsV1V2V3Aa=alengthaV1V2V3alengthV1F
itAa<V5alengthV4Aa<=c0V5Aa<V5alengthV4Aa<=c0V5a>=V5alengthV4Oa<V5c0a>=V5alengthV4INa<V5c0F
VC for defensive_get
ia=V7aV4V5V6Aa<V5alengthV7Aa<=c0V5Ia=V7aV4V5V6Aa=aeltsV7asetaeltsV4V5V6Ia=alengthV7alengthV4FAa<V5alengthV4Aa<=c0V5tAa>=V5alengthV4Oa<V5c0a>=V5alengthV4INa<V5c0F
VC for defensive_set
a=alengthamakeV4V5V4Aa=aamakeV4V5V6V5Ia<V6V4Aa<=c0V6FIa>=V4c0F
ia=aV9V11aV7V11Ia<V11alengthV9Aa<=c0V11FAa=alengthV9alengthV7Ia>c1a+V10c1Aa=aV12V13aV7V13Ia<V13alengthV12Aa<=c0V13FAa=alengthV12alengthV7Ia=aV12V14aV7V14Ia<V14a+V10c1Aa<=c0V14FAa=aV17V18aV7V18Ia<V18a+V15c1Aa<=c0V18FIa=V17aV12V15V16Aa=aeltsV17asetaeltsV12V15V16Ia=alengthV17alengthV12FAa<V15alengthV12Aa<=c0V15LaV7V15Aa<V15alengthV7Aa<=c0V15Ia=aV12V19aV7V19Ia<V19V15Aa<=c0V19FAa<=V15V10Aa<=c1V15FIa=alengthV12alengthV9FAa=aV9V20aV7V20Ia<V20c1Aa<=c0V20FIa<=c1a+V10c1La-V8c1Ia=alengthV9V8Aa=aV9V21aV7c0Ia<V21V8Aa<=c0V21FFAa>=V8c0Aa<c0alengthV7Aa<=c0c0a=aV22V23aV7V23Ia<V23alengthV22Aa<=c0V23FAa=alengthV22alengthV7Ia=alengthV22c0Fa=V8c0LalengthV7F
VC for copy
ia=aV10V12aV7a+V8V12Ia<V12V9Aa<=c0V12FAa=alengthV10V9Ia>c0a+V11c1Aa=aV13V14aV7a+V8V14Ia<V14V9Aa<=c0V14FAa=alengthV13V9Ia=aV13V15aV7a+V8V15Ia<V15a+V11c1Aa<=c0V15FAa=aV19V20aV7a+V8V20Ia<V20a+V16c1Aa<=c0V20FIa=V19aV13V16V18Aa=aeltsV19asetaeltsV13V16V18Ia=alengthV19alengthV13FAa<V16alengthV13Aa<=c0V16LaV7V17Aa<V17alengthV7Aa<=c0V17La+V8V16Ia=aV13V21aV7a+V8V21Ia<V21V16Aa<=c0V21FAa<=V16V11Aa<=c0V16FIa=alengthV13alengthV10FAa=aV10V22aV7a+V8V22Ia<V22c0Aa<=c0V22FIa<=c0a+V11c1La-V9c1Ia=alengthV10V9Aa=aV10V23aV7c0Ia<V23V9Aa<=c0V23FFAa>=V9c0Aa<c0alengthV7Aa<=c0c0a=aV24V25aV7a+V8V25Ia<V25V9Aa<=c0V25FAa=alengthV24V9Ia=alengthV24c0FAa=V9c0a=alengthV7c0Ia<=a+V8V9alengthV7Aa<=c0V9Aa<=c0V8F
VC for sub
a=aV7V12V10Ia<V12a+V8V9Aa<=V8V12FAtIa<V13alengthV7Aa<=a+V8V9V13Oa<V13V8Aa<=c0V13FIa>c0a+V11c1Aa=aV14V15V10Ia<V15a+V8V9Aa<=V8V15FAa=aV14V16aV7V16Ia<V16alengthV14Aa<=a+V8V9V16Oa<V16V8Aa<=c0V16FIa=aV14V17V10Ia<V17a+V8a+V11c1Aa<=V8V17FAa=aV14V18aV7V18Ia<V18alengthV14Aa<=a+V8V9V18Oa<V18V8Aa<=c0V18FAa=aV21V22V10Ia<V22a+V8a+V19c1Aa<=V8V22FAa=aV21V23aV7V23Ia<V23alengthV21Aa<=a+V8V9V23Oa<V23V8Aa<=c0V23FIa=V21aV14V20V10Aa=aeltsV21asetaeltsV14V20V10Ia=alengthV21alengthV14FAa<V20alengthV14Aa<=c0V20La+V8V19Ia=aV14V24V10Ia<V24a+V8V19Aa<=V8V24FAa=aV14V25aV7V25Ia<V25alengthV14Aa<=a+V8V9V25Oa<V25V8Aa<=c0V25FAa<=V19V11Aa<=c0V19FIa=alengthV14alengthV7FAa=aV7V26V10Ia<V26a+V8c0Aa<=V8V26FAtIa<V27alengthV7Aa<=a+V8V9V27Oa<V27V8Aa<=c0V27FIa<=c0a+V11c1La-V9c1Ia<=a+V8V9alengthV7Aa<=c0V9Aa<=c0V8F
VC for fill
a<=c0aofs1
a<=c0alen
a<=a+aofs1alenalengthaa1
a<=c0aofs2
a<=a+aofs2alenalengthaa2
a<=c0a+a-alenc1c1
Na<akc0Aa<=c0ak
t
loop invariant init
tINa<V7c0Aa<=c0V7F
a<=c0ak
a<akc0
a=aaa2a+aofs2akaaa1a+aofs1ak
a=alengthaa21alengthaa2
a<=c0ai
a<=aia-alenc1
a=aaa21a+aofs2V7aaa2a+aofs2V7INa<V7aiAa<=c0V7F
a=aaa21a+aofs2V8aaa1a+aofs1V8Ia<V8aiAa<=c0V8F
a<a+aofs1aialengthaa1Aa<=c0a+aofs1ai
index in array bounds
a<a+aofs2aialengthaa21Aa<=c0a+aofs2ai
a=alengthaa22alengthaa21
a=aeltsaa22asetaeltsaa21a+aofs2aiaaa1a+aofs1ai
a=aa22aaa21a+aofs2aiaaa1a+aofs1ai
Na<aka+aic1Aa<=c0ak
a=aaa22a+aofs2akaaa2a+aofs2ak
loop invariant preservation
a=aaa22a+aofs2V9aaa2a+aofs2V9INa<V9a+aic1Aa<=c0V9F
a<aka+aic1
a=aaa22a+aofs2akaaa1a+aofs1ak
a=aaa21a+aofs2V7aaa2a+aofs2V7INa<V7a+a-alenc1c1Aa<=c0V7F
a=aaa21a+aofs2V8aaa1a+aofs1V8Ia<V8a+a-alenc1c1Aa<=c0V8F
a<aialengthaa21Aa<=a+aofs2alenaiOa<aiaofs2Aa<=c0ai
a=aaa21aiaaa2ai
postcondition
a=alengthaV1V2V3alengthV1F
a=aeltsaV4V5V6asetaeltsV4V5V6F
a=aamakeV7V8V9V8Ia<V9V7Aa<=c0V9FIa>=V7c0F
a=alengthamakeV10V11V10Ia>=V10c0F
a=aaa21a+aofs2V12aaa2a+aofs2V12INa<=c0V12F
a=aaa21a+aofs2V13aaa2a+aofs2V13INa<V13a+a-alenc1c1F
a=aaa21a+aofs2V14aaa1a+aofs1V14Ia<V14a+a-alenc1c1Aa<=c0V14F
a=aaa21V15aaa2V15Ia<V15aofs2Aa<=c0V15F
a=aaa21V16aaa2V16Ia<V16alengthaa21Aa<=a+aofs2alenV16F
a<=aofs2ai
a<aia+aofs2alen
a=a@aeltsaa21aia@aeltsaa1a-a+aofs1aiaofs2
a=aaa21V9aaa2V9Ia<V9alengthaa21Aa<=a+aofs2alenV9Oa<V9aofs2Aa<=c0V9F
a=aaa21aiaaa1a-a+aofs1aiaofs2
a>c0a+a-alenc1c1
a=aaa2V7aaa1a-a+aofs1V7aofs2Ia<V7a+aofs2alenAa<=aofs2V7FAtIa<V8alengthaa2Aa<=a+aofs2alenV8Oa<V8aofs2Aa<=c0V8F
out of loop bounds
a=aV9V13aV7a-a+V8V13V10Ia<V13a+V10V11Aa<=V10V13FAtIa<V14alengthV9Aa<=a+V10V11V14Oa<V14V10Aa<=c0V14FIa>c0a+V12c1Aa=aV15V16aV7a-a+V8V16V10Ia<V16a+V10V11Aa<=V10V16FAa=aV15V17aV9V17Ia<V17alengthV15Aa<=a+V10V11V17Oa<V17V10Aa<=c0V17FIa=aV15a+V10V18aV7a+V8V18Ia<V18a+V12c1Aa<=c0V18FAa=aV15a+V10V19aV9a+V10V19INa<V19a+V12c1Aa<=c0V19FAa=aV24a+V10V25aV7a+V8V25Ia<V25a+V20c1Aa<=c0V25FAa=aV24a+V10V26aV9a+V10V26INa<V26a+V20c1Aa<=c0V26FIa=V24aV15V23V22Aa=aeltsV24asetaeltsV15V23V22Ia=alengthV24alengthV15FAa<V23alengthV15Aa<=c0V23La+V10V20LaV7V21Aa<V21alengthV7Aa<=c0V21La+V8V20Ia=aV15a+V10V27aV7a+V8V27Ia<V27V20Aa<=c0V27FAa=aV15a+V10V28aV9a+V10V28INa<V28V20Aa<=c0V28FAa<=V20V12Aa<=c0V20FIa=alengthV15alengthV9FAa=aV9a+V10V29aV7a+V8V29Ia<V29c0Aa<=c0V29FAtINa<V30c0Aa<=c0V30FIa<=c0a+V12c1La-V11c1Ia<=a+V10V11alengthV9Aa<=c0V10Aa<=a+V8V11alengthV7Aa<=c0V11Aa<=c0V8F
VC for blit
ia=aV15a+alengthV7V16aV8V16Ia<V16alengthV8Aa<=c0V16FAa=aV15V17aV7V17Ia<V17alengthV7Aa<=c0V17FAa=alengthV15a+alengthV7alengthV8Ia=aV15V18aV8a-a+c0V18V14Ia<V18a+V14V13Aa<=V14V18FAa=aV15V19aV12V19Ia<V19alengthV15Aa<=a+V14V13V19Oa<V19V14Aa<=c0V19FIa=alengthV15alengthV12FAa<=a+V14V13alengthV12Aa<=c0V14Aa<=a+c0V13alengthV8Aa<=c0V13Aa<=c0c0LalengthV7LalengthV8Ia=aV12V20aV7a-a+c0V20c0Ia<V20a+c0V11Aa<=c0V20FAa=aV12V21aV10V21Ia<V21alengthV12Aa<=a+c0V11V21Oa<V21c0Aa<=c0V21FIa=alengthV12alengthV10FAa<=a+c0V11alengthV10Aa<=c0c0Aa<=a+c0V11alengthV7Aa<=c0V11Aa<=c0c0LalengthV7Ia=alengthV10V9Aa=aV10V22aV7c0Ia<V22V9Aa<=c0V22FFAa>=V9c0La+alengthV7alengthV8Aa<c0alengthV7Aa<=c0c0a=aV23a+alengthV7V24aV8V24Ia<V24alengthV8Aa<=c0V24FAa=aV23V25aV7V25Ia<V25alengthV7Aa<=c0V25FAa=alengthV23a+alengthV7alengthV8Ia=aV23V26aV8V26Ia<V26alengthV23Aa<=c0V26FAa=alengthV23alengthV8Fa=alengthV7c0F
VC for append
ia=aV7V12aV7a-a+V8V12V9Ia<V12a+V9V10Aa<=V9V12FAtIa<V13alengthV7Aa<=a+V9V10V13Oa<V13V9Aa<=c0V13FIa>c0a+V11c1Aa=aV14V15aV7a-a+V8V15V9Ia<V15a+V9V10Aa<=V9V15FAa=aV14V16aV7V16Ia<V16alengthV14Aa<=a+V9V10V16Oa<V16V9Aa<=c0V16FIa=aV14V17aV7a-a+V8V17V9Ia<V17a+V9a+V11c1Aa<=V9V17FAa=aV14V18aV7V18Ia<V18alengthV14Aa<=a+V9a+V11c1V18Oa<V18V9Aa<=c0V18FAa=aV23V24aV7a-a+V8V24V9Ia<V24a+V9a+V19c1Aa<=V9V24FAa=aV23V25aV7V25Ia<V25alengthV23Aa<=a+V9a+V19c1V25Oa<V25V9Aa<=c0V25FIa=V23aV14V22V21Aa=aeltsV23asetaeltsV14V22V21Ia=alengthV23alengthV14FAa<V22alengthV14Aa<=c0V22La+V9V19LaV14V20Aa<V20alengthV14Aa<=c0V20La+V8V19Ia=aV14V26aV7a-a+V8V26V9Ia<V26a+V9V19Aa<=V9V26FAa=aV14V27aV7V27Ia<V27alengthV14Aa<=a+V9V19V27Oa<V27V9Aa<=c0V27FAa<=V19V11Aa<=c0V19FIa=alengthV14alengthV7FAa=aV7V28aV7a-a+V8V28V9Ia<V28a+V9c0Aa<=V9V28FAtIa<V29alengthV7Aa<=a+V9c0V29Oa<V29V9Aa<=c0V29FIa<=c0a+V11c1La-V10c1a=aV7V31aV7a-a+V8V31V9Ia<V31a+V9V10Aa<=V9V31FAtIa<V32alengthV7Aa<=a+V9V10V32Oa<V32V9Aa<=c0V32FIa<V30a-c0c1Aa=aV33V34aV7a-a+V8V34V9Ia<V34a+V9V10Aa<=V9V34FAa=a
VC for self_blit
ia=alengthV2V0Aa=aV2V4a@V1V4Ia<V4V0Aa<=c0V4FIa>c1a+V3c1Aa=alengthV5V0Aa=aV5V6a@V1V6Ia<V6V0Aa<=c0V6FIa=aV5V7a@V1V7Ia<V7a+V3c1Aa<=c0V7FAa=aV10V11a@V1V11Ia<V11a+V8c1Aa<=c0V11FIa=V10aV5V8V9Aa=aeltsV10asetaeltsV5V8V9Ia=alengthV10alengthV5FAa<V8alengthV5Aa<=c0V8La@V1V8Ia=aV5V12a@V1V12Ia<V12V8Aa<=c0V12FAa<=V8V3Aa<=c1V8FIa=alengthV5alengthV2FAa=aV2V13a@V1V13Ia<V13c1Aa<=c0V13FIa<=c1a+V3c1La-V0c1Ia=alengthV2V0Aa=aV2V14a@V1c0Ia<V14V0Aa<=c0V14FFAa>=V0c0a=alengthV15V0Aa=aV15V16a@V1V16Ia<V16V0Aa<=c0V16FIa=alengthV15c0Fa=V0c0Ia>=V0c0F
VC for init
apermut_subV0V1V4V5Ia<=V5alengthV0Ia<=c0V4Ia<V3V5Aa<=V4V3Ia<V2V5Aa<=V4V2IaexchangeV0V1V2V3F
empty_shape
apermut_subV6V8V9V10Iapermut_subV7V8V9V10Iapermut_subV6V7V9V10Ia<=V10alengthV6Ia<=c0V9F
apermut_subV11V12V15V16Ia<=V16alengthV11Aa<=V14V16Ia<=V15V13Aa<=c0V15Iapermut_subV11V12V13V14F
apermut_allV17V18IaexchangeV17V18V19V20F
aexchangeV0V6V1V2Ia=V6aV5V2V3Aa=aeltsV6asetaeltsV5V2V3Ia=alengthV6alengthV5FAa<V2alengthV5Aa<=c0V2Ia=V5aV0V1V4Aa=aeltsV5asetaeltsV0V1V4Ia=alengthV5alengthV0FAa<V1alengthV0Aa<=c0V1LaV0V2Aa<V2alengthV0Aa<=c0V2LaV0V1Aa<V1alengthV0Aa<=c0V1Ia<V2alengthV0Aa<=c0V2Aa<V1alengthV0Aa<=c0V1F
VC for swap
a<V1alengthV0Aa<=c0V1Aa<=V2alengthV0Aa>=V3c0Aa<a-V2V3a-V2V1Aa<=c0a-V2V1La+V1c1INa<=V2V1Ia<=V2alengthV0Aa>=V1c0F
VC for to_list
ia=ato_listV0V1V2aConsaV0V1ato_listV0a+V1c1V2a=ato_listV0V1V2aNila<=V2V1Ia<=V2alengthV0Aa>=V1c0F
a=a++ato_listV3V4V5ato_listV3V5V6ato_listV3V4V6Ia=a++ato_listV3V7V5ato_listV3V5V6ato_listV3V7V6La+V4c1ONa<V4V5Aa<=V6alengthV3Aa<=V5V6Aa<=V8V5Aa<=c0V8Aa<a-V5V8a-V5V4Aa<=c0a-V5V4La+V4c1Ia<V4V5Ia<=V6alengthV3Aa<=V5V6Aa<=V4V5Aa<=c0V4F
VC for to_list_append
VC for to_seq_sub
ia=ato_seq_subV0V1V2aconsaV0V1ato_seq_subV0a+V1c1V2a=ato_seq_subV0V1V2aemptya<=V2V1Ia<=V2alengthV0Aa>=V1c0F
a<a-V5V6a-V5V4Aa<=c0a-V5V4La+V4c1Ia<V4V5Ia<=V5alengthV3Aa<=V4V5Aa<=c0V4F
variant decrease
a<=V5alengthV3Aa<=V6V5Aa<=c0V6La+V4c1Ia<V4V5Ia<=V5alengthV3Aa<=V4V5Aa<=c0V4F
precondition
a=alength1ato_seq_subV3V4V5a-V5V4Ia=alength1ato_seq_subV3V6V5a-V5V6La+V4c1ONa<V4V5Ia<=V5alengthV3Aa<=V4V5Aa<=c0V4F
a=alength1ato_seq_subV3V4V5a-V5V4Ia=alength1ato_seq_subV3V6V5a-V5V6La+V4c1ONa<V4V5Aa<=V5alengthV3Aa<=V7V5Aa<=c0V7Aa<a-V5V7a-V5V4Aa<=c0a-V5V4La+V4c1Ia<V4V5Ia<=V5alengthV3Aa<=V4V5Aa<=c0V4F
VC for to_seq_length
a=alength1ato_seq_subV3V4V5a-V5V4Ia<=V5alengthV3Aa<=V4V5Aa<=c0V4F
a<a-V8V10a-V8V7Aa<=c0a-V8V7La+V7c1Ia<V7V8Ia<=V9alengthV6Aa<V8V9Aa<=V7V8Aa<=c0V7F
a<=V9alengthV6Aa<V8V9Aa<=V10V8Aa<=c0V10La+V7c1Ia<V7V8Ia<=V9alengthV6Aa<V8V9Aa<=V7V8Aa<=c0V7F
a=agetato_seq_subV6V7V9a-V8V7aV6V8Ia=agetato_seq_subV6V10V9a-V8V10aV6V8La+V7c1ONa<V7V8Ia<=V9alengthV6Aa<V8V9Aa<=V7V8Aa<=c0V7F
a=agetato_seq_subV6V7V9a-V8V7aV6V8Ia=agetato_seq_subV6V10V9a-V8V10aV6V8La+V7c1ONa<V7V8Aa<=V9alengthV6Aa<V8V9Aa<=V11V8Aa<=c0V11Aa<a-V8V11a-V8V7Aa<=c0a-V8V7La+V7c1Ia<V7V8Ia<=V9alengthV6Aa<V8V9Aa<=V7V8Aa<=c0V7F
VC for to_seq_nth
a=agetato_seq_subV6V7V9a-V8V7aV6V8Ia<=V9alengthV6Aa<V8V9Aa<=V7V8Aa<=c0V7F
a<=alengthV10alengthV10Aa>=c0c0F
VC for to_seq
ainversionV0V2a+V2c1IaexchangeV0V1V2a+V2c1Aa>aV0V2aV0a+V2c1Aa<V2a-alengthV0c1Aa<=c0V2F
assertion
NainversionV1V2a+V2c1IainversionV0V2a+V2c1IaexchangeV0V1V2a+V2c1Aa>aV0V2aV0a+V2c1Aa<V2a-alengthV0c1Aa<=c0V2F
a=anumofa@a@eainversionV5V6V7qa=a@a@a@V4V5V6V7aTrueFV1V3V3alengthV1a+a+a+anumofa@a@eainversionV9V10V11qa=a@a@a@V8V9V10V11aTrueFV1V3V3V2anumofa@a@eainversionV13V14V15qa=a@a@a@V12V13V14V15aTrueFV1V3V2a+V2c1anumofa@a@eainversionV17V18V19qa=a@a@a@V16V17V18V19aTrueFV1V3a+V2c1a+V2c2anumofa@a@eainversionV21V22V23qa=a@a@a@V20V21V22V23aTrueFV1V3a+V2c2alengthV1Ia<V3V2Aa<=c0V3FINainversionV1V2a+V2c1IainversionV0V2a+V2c1IaexchangeV0V1V2a+V2c1Aa>aV0V2aV0a+V2c1Aa<V2a-alengthV0c1Aa<=c0V2F
a=anumofa@a@eainversionV5V6V7qa=a@a@a@V4V5V6V7aTrueFV0V3V3alengthV0a+a+a+anumofa@a@eainversionV9V10V11qa=a@a@a@V8V9V10V11aTrueFV0V3V3V2anumofa@a@eainversionV13V14V15qa=a@a@a@V12V13V14V15aTrueFV0V3V2a+V2c1anumofa@a@eainversionV17V18V19qa=a@a@a@V16V17V18V19aTrueFV0V3a+V2c1a+V2c2anumofa@a@eainversionV21V22V23qa=a@a@a@V20V21V22V23aTrueFV0V3a+V2c2alengthV0Ia<V3V2Aa<=c0V3FINainversionV1V2a+V2c1IainversionV0V2a+V2c1IaexchangeV0V1V2a+V2c1Aa>aV0V2aV0a+V2c1Aa<V2a-alengthV0c1Aa<=c0V2F
a=anumofa@a@eainversionV5V6V7qa=a@a@a@V4V5V6V7aTrueFV1V3V2a+V2c1anumofa@a@eainversionV9V10V11qa=a@a@a@V8V9V10V11aTrueFV0V3a+V2c1a+V2c2Ia<V3V2Aa<=c0V3FINainversionV1V2a+V2c1IainversionV0V2a+V2c1IaexchangeV0V1V2a+V2c1Aa>aV0V2aV0a+V2c1Aa<V2a-alengthV0c1Aa<=c0V2F
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VC for exchange_inversion
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