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Proof step 53 from proof inv-format (previous step)

avol = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))], ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)) ⊦ ⟪ebm_avol_remap#(3; avol; err); m := LEB_SIZE; sb := ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)); if err = ESUCCESS then let buf = ? in {persistence_io_encode_lpt#(lpt, m; ; buf, err); if err = ESUCCESS then persistence_io_write_lebs#(sb.lpt, lptlebs(# lpt, m), buf, m; avol; err)}; m0 := EB_PAGE_SIZE; if err = ESUCCESS then persistence_io_write_superblock#(sb, m0, m; avol; err); logoff := m⟫ ( ( err = ESUCCESS → (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ sb.main + # lpt0 = # 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(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)))) ∧ m0 = EB_PAGE_SIZE ∧ m = LEB_SIZE ∧ ebm-vol-inv(avol)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr ∧ sb.maxino = m1 ∧ subarray(avol, sb.main, # avol - sb.main) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ avol[sb.log].data = mkbuf(0) ∧ avol[sb.orph].data = mkbuf(0)))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: ebm-avol-asm name: inv-remap seq: ebm-vol-inv(avol), m < # avol ⊦ ⟪ebm_avol_remap#(m; avol; err)⟫ ebm-vol-inv(avol) subst: [m, avol, err] → [3, avol, err] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ # avol[n, aleb] = # avol; (s)% ⊦ # fill(avol, aleb) = # avol; (s)% ⊦ # mkavolume(n) = n; (s)%n < n0 ⊦ (* n) < m0 + (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)%n < # avol ⊦ ebm-vol-inv(avol) → ( ebm-vol-inv(avol[n, aleb]) ↔ ( avol[n].mapped? → # avol[n].data ≤ LEB_SIZE ∧ is-aligned(# avol[n].data, EB_PAGE_SIZE)) → aleb.mapped? → # aleb.data ≤ LEB_SIZE ∧ is-aligned(# aleb.data, EB_PAGE_SIZE)); (ss)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)