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Proof step 18 from proof refine-commit (previous step)

# lpt = # lpt0, # lpt2 = # lpt0, # avol0 = # avol2, # avol2 = # lpt0 + m10, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol2[0] = mapped(buf2), avol2[m7] = mapped(buf3), avol2[m6] = mapped(buf4), subarray(avol2, m10, # lpt0) = subarray(avol0, m10, # lpt0), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m10), # lpt0), disk-layout(mksb(adr, m, m6, m7, m8, m9, m10), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(subarray(avol0, m10, # lpt0)), ebm-vol-inv(avol0), is-encoded(log, buf4), is-encoded(lpt0, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m10), buf), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded(mksb(adr, m, m6, m7, m8, m9, m10), buf2), is-encoded-pad(ns, m4, buf0), is-encoded-pad(orphans1, m8, buf3), mapped-full?(avol2, m9, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err ≠ ESUCCESS → mksb(adr, m, m6, m7, m8, m9, m10) = mksb(adr0, m0, m1, m2, m4, m5, m10) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(# lpt0, LEB_SIZE)) = lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS → adr = adr1 ∧ m = m3 ∧ buf4 = mkbuf(0) ∧ lpt0 = lpt ∧ orphans1 = ns0, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_commit#(lpt, adr1, m3, subarray(avol0, m10, # lpt0); ns0, adr0, m0, plog, lpt2, ns; err0)⟩ ( m0 = m ∧ adr0 = adr ∧ log = plog ∧ is-encoded(lpt2, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = ns0 ∧ err = err0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 19:
# avol2 = # lpt1 + m10, # avol0 = # avol2, # lpt2 = # lpt1, # lpt3 = # lpt1, avol2[m6] = mapped(buf4), avol2[m7] = mapped(buf3), avol2[0] = mapped(buf2), avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), adr = adr3, adr0 = adr1, avol = subarray(avol0, m10, # lpt1), lpt = lpt2, lpt0 = lpt3, m = m12, m0 = m3, orphans = ns0, subarray(avol2, m10, # lpt1) = subarray(avol0, m10, # lpt1), disk-layout(mksb(adr2, m11, m6, m7, m8, m9, m10), # lpt1), disk-layout(mksb(adr3, m12, m1, m2, m4, m5, m10), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m10, # lpt1)), ebm-vol-inv(avol2), is-encoded(mksb(adr2, m11, m6, m7, m8, m9, m10), buf2), is-encoded(plog, buf1), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded(mksb(adr3, m12, m1, m2, m4, m5, m10), buf), is-encoded(lpt1, lebs(avol2, m9, lptlebs(# lpt1, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans1, m8, buf3), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), mapped-full?(avol2, m9, lptlebs(# lpt1, LEB_SIZE)), m10 + # lpt1 ≤ # avol0, err1 = ESUCCESS → adr2 = adr1 ∧ m11 = m3 ∧ buf4 = mkbuf(0) ∧ lpt1 = lpt3 ∧ orphans1 = ns0, logoff ≠ LEB_SIZE → # buf1 = logoff, err1 ≠ ESUCCESS → mksb(adr2, m11, m6, m7, m8, m9, m10) = mksb(adr3, m12, m1, m2, m4, m5, m10) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(# lpt1, LEB_SIZE)) = lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ⟨if # lpt0 = # avol then {fail_or_success#(; ; err); if err = ESUCCESS then {adr := adr0; m := m0; plog := []; lpt := lpt0; ns := orphans}; orphans := ?} else abort⟩ ( m = m11 ∧ adr = adr2 ∧ log = plog ∧ is-encoded(lpt, lebs(avol2, m9, lptlebs(# lpt1, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = orphans ∧ err1 = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_io_commit# (LPT, PROOTADR0, PMAXINO0, PVOL ; ORPHANS, PROOTADR, PMAXINO, PLOG, PLPT, PORPHANS ; ERR ) {if # LPT = # PVOL then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then {PROOTADR := PROOTADR0; PMAXINO := PMAXINO0; PLOG := []; PLPT := LPT; PORPHANS := ORPHANS}; ORPHANS := ?} else abort };% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)%# avol = sb.main + mainareasize ⊦ disk-layout(sb, mainareasize) → # avol ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s)