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Proof step 77 from proof inv-format (previous step)

m = LEB_SIZE, sb = ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), ebm-vol-inv(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-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), err = ESUCCESS → is-encoded(lpt, buf) ∧ # buf = lptsize(# lpt, LEB_SIZE), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪avol := fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]; 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)))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 78:
avol = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))], m = LEB_SIZE, sb = ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), 3 < # fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))], 1 < # fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped), ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)), ebm-vol-inv(fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[1, mapped(mkbuf(0))]), err = ESUCCESS → is-encoded(lpt, buf) ∧ # buf = lptsize(# lpt, LEB_SIZE), err = ESUCCESS ∨ ⌊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)))

Rule argument

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)