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Proof step 231 from proof refine-rename-new-keep-parent (previous step)

abs-dirs(fs0, ri0)[m3].nsubdirs = 0, fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), fs0[ri0[inodekey(m)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)]), log-cons(log0, fs0), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m3) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m3, str)] ∈ fs0, 1 ≤ m6, 1 ≤ m5, boolvar3 → boolvar4, m4 ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, m5 = 0, m6 = 0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], dentrykey(m3, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m3, str), m4 = 0 ∧ m3 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 232:
fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, true, m4, m5, m6), fs0[ri0[dentrykey(m3, str)]] = dentrynode(key1, m), abs-dirs(fs0, ri0)[m3] = mkdir(m0, md, m1, m2, entries), m2 = 0, fs0[ri0[inodekey(m)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj((ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)][adr3, inodenode(inodekey(m3), md0, true, m4, m5, m6)], (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2][inodekey(m3), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, 1 ≤ m5, 1 ≤ m6, boolvar3 → boolvar4, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, m4 ≠ 0 ∨ m3 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m3 = 0, m5 = 0, m6 = 0, adr2 ∈ ri0 -- dentrykey(m3, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m3, str0) ∈ ri0, adr3 ∈ (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], m4 = 0 ∧ m3 ≠ ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dirs(fs0, ri0)[m3], m0, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dirs(fs0, ri0)[m3], m0, md, m1, m2, entries