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Proof step 208 from proof inv-commit (previous step)

# lpt0 = # lpt, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol, avol[0] = mapped(buf), avol[4] = mapped(buf0), avol[2] = mapped(buf1), avol1 = avol, m = 1, ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ [if m < # avol then {fail_or_success#(; ; err); if err = ESUCCESS then avol[m] := mapped(mkbuf(0)) else {skip or avol[m] := unmapped}} else abort] ( ebm-vol-inv(avol) → ⟪ns := orphans; m1 := EB_PAGE_SIZE; sb1 := mksb(adr, m3, 1, 3, # orphans, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)); m0 := LEB_SIZE; if err = ESUCCESS then persistence_io_write_orphans#(sb1.orph, m1, m0; orphans, avol; err); if err = ESUCCESS then let buf = ? in {persistence_io_encode_lpt#(lpt, m0; ; buf, err); if err = ESUCCESS then persistence_io_write_lebs#(sb1.lpt, lptlebs(# lpt, m0), buf, m0; avol; err)}; if err = ESUCCESS then ebm_avol_sync_device#(avol; ; err); if err = ESUCCESS then persistence_io_write_superblock#(sb1, m1, m0; avol; err); sb0 := mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)); if err = ESUCCESS then {sb0 := sb1; logoff := 0}⟫ ( (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb0, avol[0].data) ∧ avol[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol[sb0.orph].data) ∧ avol[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb0.log].data = logoff) ∧ is-encoded(log, avol[sb0.log].data) ∧ mapped-full?(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m3 ∧ avol[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb0.orphsize, avol[sb0.orph].data)) ∧ ( err ≠ ESUCCESS → sb0 = mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), sb0.main) ∧ avol[2] = avol1[2] ∧ avol[4] = avol1[4] ∧ lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol - sb0.main, LEB_SIZE)) = lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ sb0.main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol = # avol1 ∧ subarray(avol, sb0.main, # avol - sb0.main) = subarray(avol1, sb0.main, # avol - sb0.main)))

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 209:
# lpt0 = # lpt, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol, avol[2] = mapped(buf1), avol[4] = mapped(buf0), avol[0] = mapped(buf), avol1 = avol, m = 1, ebm-vol-inv(avol), is-encoded(mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt0, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then avol[m] := mapped(mkbuf(0)) else {skip or avol[m] := unmapped}] ( ebm-vol-inv(avol) → ⟪ns := orphans; m1 := EB_PAGE_SIZE; sb1 := mksb(adr, m3, 1, 3, # orphans, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)); m0 := LEB_SIZE; if err = ESUCCESS then persistence_io_write_orphans#(sb1.orph, m1, m0; orphans, avol; err); if err = ESUCCESS then let buf = ? in {persistence_io_encode_lpt#(lpt, m0; ; buf, err); if err = ESUCCESS then persistence_io_write_lebs#(sb1.lpt, lptlebs(# lpt, m0), buf, m0; avol; err)}; if err = ESUCCESS then ebm_avol_sync_device#(avol; ; err); if err = ESUCCESS then persistence_io_write_superblock#(sb1, m1, m0; avol; err); sb0 := mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)); if err = ESUCCESS then {sb0 := sb1; logoff := 0}⟫ ( (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb0, avol[0].data) ∧ avol[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol[sb0.orph].data) ∧ avol[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb0.log].data = logoff) ∧ is-encoded(log, avol[sb0.log].data) ∧ mapped-full?(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m3 ∧ avol[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb0.orphsize, avol[sb0.orph].data)) ∧ ( err ≠ ESUCCESS → sb0 = mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), sb0.main) ∧ avol[2] = avol1[2] ∧ avol[4] = avol1[4] ∧ lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol - sb0.main, LEB_SIZE)) = lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ sb0.main = 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ # avol = # avol1 ∧ subarray(avol, sb0.main, # avol - sb0.main) = subarray(avol1, sb0.main, # avol - sb0.main)))

Rule argument

pos: right 1

Additional information

Used simplifier rules: nat-stuff2: ⊦ n = 5 + n1 → n ≠ 0;%nat-stuff3: ⊦ n = 5 + n1 → n ≠ 1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic