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Proof step 86 from proof inv-recover (previous step)

m8 + # lpt0 = # avol1, avol1[m10] = mapped(buf1), avol1[m5] = mapped(buf0), avol1[0] = mapped(buf), m10 < # avol2, disk-layout(mksb(adr0, m9, m10, m5, m6, m7, m8), # lpt0), ebm-vol-inv(avol1), is-encoded(lpt0, lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded(mksb(adr0, m9, m10, m5, m6, m7, m8), buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol1, m7, lptlebs(# lpt0, LEB_SIZE)), m8 ≤ # avol1, avol1 ⊆ avol2, m3 ≠ LEB_SIZE → # buf1 = m3 ⊦ ⟪persistence_io_read_orphans#(mksb(adr0, m9, m10, m5, m6, m7, m8), avol2; orphans; err); if err ≠ ESUCCESS then debug#("persistence-io: reading orphans failed"); m0 := LEB_SIZE; sb := mksb(adr0, m9, m10, m5, m6, m7, m8); if err = ESUCCESS then {m := # avol2 - sb.main; let buf = ? in {persistence_io_read_lebs#(sb.lpt, lptlebs(m, m0), m0, avol2; ; buf, err); if err = ESUCCESS then {lpt := mklparray(m); lpt := fill(lpt, mklp(0, 0, LP_FREE, 0)); persistence_io_decode_lpt#(buf; lpt, err)}; if err ≠ ESUCCESS then debug#("persistence-io: reading LPT failed")}}; if err = ESUCCESS then {logoff := m0; adr := sb.indexaddr; m2 := sb.maxino}⟫ ( ( err = ESUCCESS → (∃ lpt1, log1, orphans1. disk-layout(sb, # lpt1) ∧ sb.main + # lpt1 = # avol1 ∧ is-encoded(sb, buf) ∧ avol2[sb.orph].mapped? ∧ is-encoded-pad(orphans1, sb.orphsize, avol2[sb.orph].data) ∧ avol2[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol2[sb.log].data = logoff) ∧ is-encoded(log1, avol2[sb.log].data) ∧ mapped-full?(avol2, sb.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol2, sb.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ m0 = LEB_SIZE) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → adr = adr0 ∧ m2 = m9 ∧ # lpt = # lpt0 ∧ is-encoded(lpt, lebs(avol2, m7, lptlebs(# lpt, LEB_SIZE))) ∧ lebs(avol2, m7, lptlebs(# lpt, LEB_SIZE)) = lebs(avol1, m7, lptlebs(# lpt, LEB_SIZE)) ∧ orphans0 = orphans))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-read-orphans seq: persistence-io-inv(sb, logoff, avol, lpt, log, orphans0), ebm-vol-inv(avol) ⊦ ⟪persistence_io_read_orphans#(sb, avol; orphans; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0)) subst: [avol, sb, orphans, err, logoff, lpt, log, orphans0] → [avol2, mksb(adr0, m9, m10, m5, m6, m7, m8), orphans, err, m3, lpt0, log0, orphans0] flags: <all paths>

Additional information

Used simplifier rules: avol-down-size: ⊦ m = # avol0 ∧ avol0 ⊆ avol1 → (n = # avol1 ↔ n = m);%avol-down-mapped-eq: n < # avol0 ⊦ avol0 ⊆ avol1 ∧ avol0[n] = mapped(buf) ∧ ebm-vol-inv(avol0) → avol1[n] = mapped(buf);%⊦ persistence-io-inv(sb, logoff, avol, lpt, log, orphans) ↔ (∃ mainareasize. disk-layout(sb, mainareasize) ∧ sb.main + mainareasize = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ avol[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb.log].data = logoff) ∧ is-encoded(log, avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)) ∧ # lpt = mainareasize ∧ is-encoded (lpt, lebs(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)))); (s)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)%# avol = sb.main + mainareasize ⊦ disk-layout(sb, mainareasize) → # avol ≠ 0; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph = m1; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ m6 + # lpt = # avol ∧ disk-layout(mksb(adr0, m1, m2, m3, m4, m5, m6), # lpt) → ¬ # avol ≤ m3; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize = m2; (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).log = m0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)%⊦ avol0 ⊆ avol1 ∧ mapped-full?(avol0, n, m) → mapped-full?(avol1, n, m); (s)% ⊦ avol1 ⊆ avol0 ∧ ebm-vol-inv(avol1) → ebm-vol-inv(avol0); (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ avol0 ⊆ avol1 → ¬ # avol0 < # avol1; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → ¬ m4 + n < m3 + lptlebs(mainareasize, LEB_SIZE); (s)%n + m ≤ # avol0 ⊦ mapped-full?(avol0, n, m) ∧ avol0 ⊆ avol1 → lebs(avol1, n, m) = lebs(avol0, n, m); (s)