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Proof step 111 from proof inv-recover (previous step)

m8 + # lpt0 = # avol1, avol1[0] = mapped(buf2), avol1[m5] = mapped(buf0), avol1[m10] = mapped(buf1), m10 < # avol2, disk-layout(mksb(adr0, m9, m10, m5, m6, m7, m8), # lpt0), ebm-vol-inv(avol1), is-encoded(mksb(adr0, m9, m10, m5, m6, m7, m8), buf2), is-encoded(log0, buf1), is-encoded(lpt0, lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE))), 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_lebs#(m7, lptlebs(# lpt0, LEB_SIZE), LEB_SIZE, avol2; ; buf, err); sb := mksb(adr0, m9, m10, m5, m6, m7, m8); if err = ESUCCESS then {lpt := mklparray(# avol2 - sb.main); 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"); m0 := LEB_SIZE; 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, buf2) ∧ 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))))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: prepost-read-lebs seq: ebm-vol-inv(avol), n + m ≤ # avol, mapped-full?(avol, n, m) ⊦ ⟪persistence_io_read_lebs# (n, m, LEB_SIZE, avol; ; buf, err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → buf = lebs(avol, n, m))) subst: [avol, m, n, err, buf] → [avol2, lptlebs(# lpt0, LEB_SIZE), m7, err, buf] flags: List([[1,0,0]])

Additional information

Used simplifier rules: avol-down-size-le: ⊦ avol0 ⊆ avol1 → (n ≤ # avol1 ↔ n ≤ # avol0);% ⊦ avol1 ⊆ avol0 ∧ ebm-vol-inv(avol1) → ebm-vol-inv(avol0); (s)%⊦ avol0 ⊆ avol1 ∧ mapped-full?(avol0, n, m) → mapped-full?(avol1, n, m); (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%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → ¬ m4 + n < m3 + lptlebs(mainareasize, LEB_SIZE); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic