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Proof step 12 from proof refine-add-log-leb (previous step)

# avol = # lpt0 + m5, avol[0] = mapped(buf), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), subarray(avol2, m5, # lpt0) = subarray(avol, m5, # lpt0), disk-layout(mksb(adr, m, m0, m1, m3, m4, m5), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(avol), ebm-vol-inv(subarray(avol, m5, # lpt0)), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)), m5 ≤ # avol, err = ESUCCESS → # avol = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m0].data = logoff0) ∧ is-encoded(plog + m2 ', avol2[m0].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), err ≠ ESUCCESS → # avol = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m0, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m0].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m0].data = logoff0) ∧ is-encoded(plog, avol2[m0].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_add_log_leb#(m2, adr, m, subarray(avol, m5, # lpt0), lpt0, orphans; plog; err0)⟩ ( # avol2 = m5 + (# avol2 - m5) ∧ subarray(avol, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(plog, avol2[m0].data) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ err = err0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 13:
# avol0 = # lpt0 + m5, avol0[m6] = mapped(buf1), avol0[m1] = mapped(buf0), avol0[0] = mapped(buf), avol = subarray(avol0, m5, # lpt0), lpt = lpt0, m0 = m2, ns = orphans, subarray(avol2, m5, # lpt0) = subarray(avol0, m5, # lpt0), disk-layout(mksb(adr, m, m6, m1, m3, m4, m5), # lpt0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), ebm-vol-inv(avol0), ebm-vol-inv(avol2), is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt0, LEB_SIZE)), m5 + # lpt0 ≤ # avol0, m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, err1 ≠ ESUCCESS → # avol0 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m6].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m6].data = logoff0) ∧ is-encoded(plog, avol2[m6].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), err1 = ESUCCESS → # avol0 = # avol2 ∧ avol2[0].mapped? ∧ is-encoded(mksb(adr, m, m6, m1, m3, m4, m5), avol2[0].data) ∧ avol2[m1].mapped? ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ avol2[m6].mapped? ∧ (logoff0 ≠ LEB_SIZE → # avol2[m6].data = logoff0) ∧ is-encoded(plog + m2 ', avol2[m6].data) ∧ mapped-full?(avol2, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# lpt0, LEB_SIZE))), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then plog := plog + m0⟩ ( # avol2 = m5 + (# avol2 - m5) ∧ subarray(avol0, m5, # lpt0) = subarray(avol2, m5, # avol2 - m5) ∧ is-encoded(plog, avol2[m6].data) ∧ is-encoded(lpt0, lebs(avol2, m4, lptlebs(# avol2 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol2[m1].data) ∧ err1 = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_io_add_log_leb# (LNUM, PROOTADR, PMAXINO, PVOL, PLPT, PORPHANS; PLOG; ERR) {fail_or_success#(; ; ERR); if ERR = ESUCCESS then PLOG := PLOG + LNUM };% ⊦ 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%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ 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)