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Proof step 11 from proof initialization (previous step)

err = ESUCCESS, err = ESUCCESS → disk-layout(mksb(adr0, m2, m4, m5, m7, m8, m9), # lpt) ∧ m9 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr0, m2, m4, m5, m7, m8, m9), avol[0].data) ∧ avol[m5].mapped? ∧ is-encoded-pad(orphans, m7, avol[m5].data) ∧ avol[m4].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m4].data = logoff) ∧ is-encoded(log, avol[m4].data) ∧ mapped-full?(avol, m8, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))) ∧ m0 = EB_PAGE_SIZE ∧ m = LEB_SIZE ∧ ebm-vol-inv(avol), err = ESUCCESS → adr0 = adr1 ∧ m2 = m3 ∧ subarray(avol, m9, # avol - m9) = fill(mkavolume(# lpt0), unmapped) ∧ is-encoded(lpt0, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))) ∧ avol[m4].data = mkbuf(0) ∧ avol[m5].data = mkbuf(0), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = m2 ∧ adr2 = adr0 ∧ # avol = m9 + (# avol - m9) ∧ avol1 = subarray(avol, m9, # avol - m9) ∧ is-encoded(plog, avol[m4].data) ∧ is-encoded(lpt1, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))) ∧ is-encoded-pad(ns0, m7, avol[m5].data) ∧ ESUCCESS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
m9 + # lpt = # avol, avol[0] = mapped(buf), avol[m5] = mapped(mkbuf(0)), avol[m4] = mapped(mkbuf(0)), subarray(avol, m9, # avol - m9) = fill(mkavolume(# lpt0), unmapped), disk-layout(mksb(adr1, m3, m4, m5, 0, m8, m9), # lpt), ebm-vol-inv(avol), is-encoded(lpt, lebs(avol, m8, lptlebs(# lpt, LEB_SIZE))), is-encoded(lpt0, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))), is-encoded(mksb(adr1, m3, m4, m5, 0, m8, m9), buf), mapped-full?(avol, m8, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → 0 = logoff ⊦ ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = m3 ∧ adr2 = adr1 ∧ avol1 = subarray(avol, m9, # avol - m9) ∧ [] = plog ∧ is-encoded(lpt1, lebs(avol, m8, lptlebs(# avol - m9, LEB_SIZE))) ∧ ∅ = ns0 ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ # mkbuf(n) = n; (s)% ⊦ is-encoded(nx, mkbuf(0)) ↔ nx = []; (s)% ⊦ is-encoded-pad(ns, n, mkbuf(0)) ↔ ns = ∅ ∧ n = 0; (s)% ⊦ mapped(buf).data = buf; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)