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Proof step 92 from proof inv-format (previous step)

# buf = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, # buf = lptsize(# lpt, LEB_SIZE), avol = 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)[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))]), is-encoded(lpt, buf) ⊦ ∀ avol, err. (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # avol = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE) ∧ ebm-vol-inv(avol) ∧ avol[0] = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[0] ∧ avol[1] = mapped(mkbuf(0)) ∧ avol[2] = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[2] ∧ avol[3] = mapped(mkbuf(0)) ∧ avol[4] = fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped)[4] ∧ 5 ≤ # avol ∧ range= (avol, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE)), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), # avol - 5 + lptlebs(# lpt, LEB_SIZE)) ∧ (err = ESUCCESS → lebs(avol, 5, lptlebs(# lpt, LEB_SIZE)) = buf ∧ mapped-full?(avol, 5, lptlebs(# lpt, LEB_SIZE))) → ⟪m0 := EB_PAGE_SIZE; sb := ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)); m := LEB_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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
# buf = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, # buf = lptsize(# lpt, LEB_SIZE), # avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol0[3] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), is-encoded(lpt, buf), range= (avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), # avol0 - 5 + lptlebs(# lpt, LEB_SIZE)), 5 ≤ # avol0, err = ESUCCESS → lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = buf ∧ mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪m0 := EB_PAGE_SIZE; sb := ((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)); m := LEB_SIZE; if err = ESUCCESS then persistence_io_write_superblock#(sb, m0, m; avol0; err); logoff := m⟫ ( ( err = ESUCCESS → (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ sb.main + # lpt0 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(sb, avol0[0].data) ∧ avol0[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol0[sb.orph].data) ∧ avol0[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[sb.log].data = logoff) ∧ is-encoded(log, avol0[sb.log].data) ∧ mapped-full?(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE)))) ∧ m0 = EB_PAGE_SIZE ∧ m = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr ∧ sb.maxino = m1 ∧ subarray(avol0, sb.main, # avol0 - sb.main) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ avol0[sb.log].data = mkbuf(0) ∧ avol0[sb.orph].data = mkbuf(0)))

Rule argument

Additional information

Used simplifier rules: nat-stuff2: ⊦ n = 5 + n1 → n ≠ 0;%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat