0specs/Mondex-refine/proofs/3349522286dom-cfin-def⊦ (∃ balance', lost'. cfin(balance, exLog, status, nextSeqNo, pdAuth, ether, balance', lost')) ↔ (∃ balance1, lost1. cfin(balance, exLog, status, nextSeqNo, pdAuth, ether, balance1, lost1))01dom-cfin-def-proofdom-cfin-def-proof-infodom-afin-def ⊦ (∃ balance', lost'. afin(balance0, lost0, balance', lost')) ↔ (∃ balance1, lost1. afin(balance0, lost0, balance1, lost1))01dom-afin-def-proofdom-afin-def-proof-infocinv-okCINV(balance, exLog, status, nextSeqNo, pdAuth, ether), COP(mi)(msg, balance, exLog, status, nextSeqNo, pdAuth, ether, balance', exLog', status', nextSeqNo', pdAuth', ether', dum0) ⊦ CINV(balance', exLog', status', nextSeqNo', pdAuth', ether')ACK-CINVVAL-CINVREQ-CINVSTARTTO-CINVSTARTFROM-CINVINCREASE-CINVABORT-CINVCINV-botLOSEMSG-CINV16181cinv-ok-proofcinv-ok-proof-infoinit-stateCINV(balance, exLog, status, nextSeqNo, pdAuth, ether), ACINV(balance, exLog, status, pdAuth, balance0, lost0) ⊦ true01init-state-proofinit-state-proof-infototal-init-state ⊦ ∃ balance, exLog, status, nextSeqNo, pdAuth, ether. CINV(balance, exLog, status, nextSeqNo, pdAuth, ether)1528total-init-state-prooftotal-init-state-proof-infodom-cop-def⊦ (∃ balance', exLog', status', nextSeqNo', pdAuth', ether', dum. cop(msg, balance, exLog, status, nextSeqNo, pdAuth, ether, balance', exLog', status', nextSeqNo', pdAuth', ether', dum)) ↔ (∃ dum0, balance', exLog', status', nextSeqNo', pdAuth', ether'. cop(msg, balance, exLog, status, nextSeqNo, pdAuth, ether, balance', exLog', status', nextSeqNo', pdAuth', ether', dum0))15dom-cop-def-proofdom-cop-def-proof-infototal-fin-stateCINV(balance, exLog, status, nextSeqNo, pdAuth, ether) ⊦ ∃ balance1, lost1. ∃ maybelost, definitelylost. balance = balance1 ∧ maybeLost(exLog, pdAuth, status, maybelost) ∧ definitelyLost(exLog, pdAuth, status, definitelylost) ∧ lost1 = (λ na. Σ filter(λ pd. pd .from = na, definitelylost ∪ maybelost))exists-definitelylostexists-maybelost48total-fin-state-prooftotal-fin-state-proof-infocorr-applCINV(balance, exLog, status, nextSeqNo, pdAuth, ether), ¬ (∃ balance', exLog', status', nextSeqNo', pdAuth', ether', dum. COP(mi)(msg, balance, exLog, status, nextSeqNo, pdAuth, ether, balance', exLog', status', nextSeqNo', pdAuth', ether', dum)) ⊦ ∃ balance0, lost0, ain. ACINV(balance, exLog, status, pdAuth, balance0, lost0) ∧ true ∧ ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null)) ∧ ¬ (∃ balance', lost', dum. AOP(mi)(ain, balance0, lost0, balance', lost', dum))46210corr-appl-proofcorr-appl-proof-infofinal-stateCINV(balance, exLog, status, nextSeqNo, pdAuth, ether), ∃ maybelost, definitelylost. balance = balance1 ∧ maybeLost(exLog, pdAuth, status, maybelost) ∧ definitelyLost(exLog, pdAuth, status, definitelylost) ∧ lost1 = (λ na. Σ filter(λ pd. pd .from = na, definitelylost ∪ maybelost)) ⊦ ∃ balance0, lost0. true ∧ ACINV(balance, exLog, status, pdAuth, balance0, lost0) ∧ balance0 = balance1 ∧ lost0 = lost147final-state-prooffinal-state-proof-infodom-aop-def⊦ (∃ balance', lost', dum. aop(ain, balance0, lost0, balance', lost', dum)) ↔ (∃ dum1, balance'0, lost'. aop(ain, balance0, lost0, balance'0, lost', dum1))15dom-aop-def-proofdom-aop-def-proof-infocorrectnessCINV(balance, exLog, status, nextSeqNo, pdAuth, ether), COP(mi)(msg, balance, exLog, status, nextSeqNo, pdAuth, ether, balance', exLog', status', nextSeqNo', pdAuth', ether', dum0), ACINV(balance', exLog', status', pdAuth', balance'0, lost'), true, true, ∀ balance0, lost0, ain. ACINV(balance, exLog, status, pdAuth, balance0, lost0) ∧ true ∧ ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null)) → (∃ balance', lost', dum. AOP(mi)(ain, balance0, lost0, balance', lost', dum)) ⊦ ∃ balance0, lost0, ain. ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null)) ∧ ACINV(balance, exLog, status, pdAuth, balance0, lost0) ∧ true ∧ AOP(mi)(ain, balance0, lost0, balance'0, lost', dum1)ACK-ACINVVAL-ACINVREQ-CINVREQ-ACINVSTARTTO-ACINVSTARTFROM-ACINVABORT-CINVABORT-ACINV43264correctness-proofcorrectness-proof-infototal-fin-output ⊦ ∃ dum. true01total-fin-output-prooftotal-fin-output-proof-infoainv-oktrue, AOP(mi)(ain, balance0, lost0, balance'0, lost', dum1) ⊦ true01ainv-ok-proofainv-ok-proof-infofinal-outputtrue ⊦ ∃ dum1. true ∧ true01final-output-prooffinal-output-proof-infoinit-inputain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null)), ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null)) ⊦ ain = ain01init-input-proofinit-input-proof-infototal-init-input ⊦ ∃ msg. ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null))24total-init-input-prooftotal-init-input-proof-infototal-input ⊦ ∃ ain. ain = ((isreq(msg) ⊃ Transfer(msg .pd .from, msg .pd .to, msg .pd .value); null))01total-input-prooftotal-input-proof-infoinit-cinvCINV(balance, exLog, status, nextSeqNo, pdAuth, ether) ⊦ CINV(balance, exLog, status, nextSeqNo, pdAuth, ether)01init-cinv-proofinit-cinv-proof-infoinit-ainvtrue ⊦ true01init-ainv-proofinit-ainv-proof-infoABORT-ACINV〈ABORT#(receiver, pdAuth; exLog, status, nextSeqNo, outmsg)〉 (exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ outmsg = outmsg'), ACINV(balance, exLog', status', pdAuth, balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver) ⊦ ACINV(balance, exLog, status, pdAuth, balance0, lost0)19120ABORT-ACINV-proofABORT-ACINV-proof-infoABORT-CINV〈ABORT#(receiver, pdAuth; exLog, status, nextSeqNo, outmsg)〉 (exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ outmsg = outmsg'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver) ⊦ outmsg' = ⊥ ∧ status'(receiver) = idle ∧ CINV(balance, exLog', status', nextSeqNo', pdAuth, ether)CINV-botINCREASE-CINV21125ABORT-CINV-proofABORT-CINV-proof-infoACK-ACINV〈ACK#(ack(pdAuth(receiver)), receiver, pdAuth, ether; status, outmsg)〉 (status = status' ∧ outmsg = outmsg'), ACINV(balance, exLog, status', pdAuth, balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver), ack(pdAuth(receiver)) ∈ ether, status(receiver) = epa ⊦ ACINV(balance, exLog, status, pdAuth, balance0, lost0)538ACK-ACINV-proofACK-ACINV-proof-infoACK-CINV〈ACK#(msg, receiver, pdAuth, ether; status, outmsg)〉 (outmsg = outmsg' ∧ status = status'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), isack(msg), authentic(receiver), msg ∈ ether, msg .pd = pdAuth(receiver), status(receiver) = epa ⊦ outmsg' = ⊥ ∧ CINV(balance, exLog, status', nextSeqNo, pdAuth, ether)237ACK-CINV-proofACK-CINV-proof-infoCINV-bot ⊦ CINV(balance', exLog', status', nextSeqNo', pdAuth', ether ++ ⊥) ↔ CINV(balance', exLog', status', nextSeqNo', pdAuth', ether)726CINV-bot-proofCINV-bot-proof-infolocalsimpINCREASE-CINV〈INCREASE#(receiver; nextSeqNo, outmsg)〉 (nextSeqNo = nextSeqNo' ∧ outmsg = outmsg'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver) ⊦ CINV(balance, exLog, status, nextSeqNo', pdAuth, ether ++ outmsg')CINV-bot241INCREASE-CINV-proofINCREASE-CINV-proof-infoLOSEMSG-CINV〈LOSEMSG#(outmsg; ether)〉 ether = ether', CINV(balance, exLog, status, nextSeqNo, pdAuth, ether ++ outmsg) ⊦ CINV(balance, exLog, status, nextSeqNo, pdAuth, ether')219LOSEMSG-CINV-proofLOSEMSG-CINV-proof-infoREQ-ACINV〈REQ#(req(pdAuth(receiver)), receiver, pdAuth, ether; balance, status, outmsg)〉 (balance = balance' ∧ status = status' ∧ outmsg = outmsg'), ACINV(balance', exLog, status', pdAuth, balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver), req(pdAuth(receiver)) ∈ ether, status(receiver) = epr ⊦ ∃ balance1, lost1. ACINV(balance, exLog, status, pdAuth, balance1, lost1) ∧ 〈ABTRANSFER#(pdAuth(receiver) .value, pdAuth(receiver) .from, pdAuth(receiver) .to; balance1, lost1)〉 (balance1 = balance0 ∧ lost1 = lost0)83261REQ-ACINV-proofREQ-ACINV-proof-infoREQ-CINV〈REQ#(msg, receiver, pdAuth, ether; balance, status, outmsg)〉 (outmsg = outmsg' ∧ balance = balance' ∧ status = status'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), isreq(msg), authentic(receiver), msg ∈ ether, msg .pd = pdAuth(receiver), status(receiver) = epr ⊦ CINV(balance', exLog, status', nextSeqNo, pdAuth, ether ++ outmsg')1056REQ-CINV-proofREQ-CINV-proof-infoSTARTFROM-ACINV〈STARTFROM#(msg, receiver, balance, ether; exLog, status, nextSeqNo, pdAuth, outmsg)〉 (exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ pdAuth = pdAuth' ∧ outmsg = outmsg'), ACINV(balance, exLog', status', pdAuth', balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver), isStartFrom(msg), status(receiver) = idle ⊦ ACINV(balance, exLog, status, pdAuth, balance0, lost0)ABORT-ACINVABORT-CINV248STARTFROM-ACINV-proofSTARTFROM-ACINV-proof-infoSTARTFROM-CINV〈STARTFROM#(msg, receiver, balance, ether; exLog, status, nextSeqNo, pdAuth, outmsg)〉 (outmsg = outmsg' ∧ exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ pdAuth = pdAuth'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), isStartFrom(msg), authentic(receiver), msg ∈ ether ⊦ CINV(balance, exLog', status', nextSeqNo', pdAuth', ether ++ outmsg')ABORT-CINVCINV-bot577STARTFROM-CINV-proofSTARTFROM-CINV-proof-infoSTARTTO-ACINV〈STARTTO#(msg, receiver, ether; exLog, status, nextSeqNo, pdAuth, outmsg)〉 (exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ pdAuth = pdAuth' ∧ outmsg = outmsg'), ACINV(balance, exLog', status', pdAuth', balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver), isStartTo(msg), status(receiver) = idle ⊦ ACINV(balance, exLog, status, pdAuth, balance0, lost0)ABORT-ACINVABORT-CINV759STARTTO-ACINV-proofSTARTTO-ACINV-proof-infoSTARTTO-CINV〈STARTTO#(msg, receiver, ether; exLog, status, nextSeqNo, pdAuth, outmsg)〉 (outmsg = outmsg' ∧ exLog = exLog' ∧ status = status' ∧ nextSeqNo = nextSeqNo' ∧ pdAuth = pdAuth'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), isStartTo(msg), authentic(receiver), msg ∈ ether ⊦ CINV(balance, exLog', status', nextSeqNo', pdAuth', ether ++ outmsg')ABORT-CINVCINV-bot790STARTTO-CINV-proofSTARTTO-CINV-proof-infoVAL-ACINV〈VAL#(val(pdAuth(receiver)), receiver, pdAuth, ether; balance, status, outmsg)〉 (balance = balance' ∧ status = status' ∧ outmsg = outmsg'), ACINV(balance', exLog, status', pdAuth, balance0, lost0), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), authentic(receiver), val(pdAuth(receiver)) ∈ ether, status(receiver) = epv ⊦ ACINV(balance, exLog, status, pdAuth, balance0, lost0)1263VAL-ACINV-proofVAL-ACINV-proof-infoVAL-CINV〈VAL#(msg, receiver, pdAuth, ether; balance, status, outmsg)〉 (outmsg = outmsg' ∧ balance = balance' ∧ status = status'), CINV(balance, exLog, status, nextSeqNo, pdAuth, ether), isval(msg), authentic(receiver), msg ∈ ether, msg .pd = pdAuth(receiver), status(receiver) = epv ⊦ CINV(balance', exLog, status', nextSeqNo, pdAuth, ether ++ outmsg')542VAL-CINV-proofVAL-CINV-proof-infoexists-definitelylostlogsfin(exLog) ⊦ ∃ definitelylost. definitelyLost(exLog, pdAuth, status, definitelylost)exists-definitelylost-aux613exists-definitelylost-proofexists-definitelylost-proof-infoexists-definitelylost-aux∀ pd. pd ∈ pds → toLogged(pd, exLog) ⊦ ∃ definitelylost. ∀ pd. pd ∈ definitelylost ↔ pd ∈ pds ∧ toLogged(pd, exLog) ∧ (fromLogged(pd, exLog) ∨ fromInEpa(pd, pdAuth, status))1119exists-definitelylost-aux-proofexists-definitelylost-aux-proof-infoexists-maybelost ⊦ ∃ maybelost. maybeLost(exLog, pdAuth, status, maybelost)exists-maybelost-auxfinite-toInEpv815exists-maybelost-proofexists-maybelost-proof-infoexists-maybelost-aux∀ pd. pd ∈ pds → toInEpv(pd, pdAuth, status) ⊦ ∃ maybelost. ∀ pd. pd ∈ maybelost ↔ pd ∈ pds ∧ toInEpv(pd, pdAuth, status) ∧ (fromLogged(pd, exLog) ∨ fromInEpa(pd, pdAuth, status))1018exists-maybelost-aux-proofexists-maybelost-aux-proof-infofinite-toInEpv ⊦ ∃ pds. ∀ pd. pd ∈ pds ↔ toInEpv(pd, pdAuth, status)finite-toInEpv-aux614finite-toInEpv-prooffinite-toInEpv-proof-infofinite-toInEpv-aux∀ na. na ∈ nas → authentic(na) ⊦ ∃ pds. ∀ pd. pd ∈ pds ↔ pd .to ∈ nas ∧ toInEpv(pd, pdAuth, status)1018finite-toInEpv-aux-prooffinite-toInEpv-aux-proof-info