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Proof step 63 from proof refine-mkdir (previous step)

fs1[ri[inodekey(m3)]] = inodenode(key, md1, true, m, m4, m5), adr4 = adr5, c_inode = p_inode1, dent = negdentry(str), dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs1[adr1, nd1][adr2, nd0][adr3, nd], fs0 = fs1, log = ((log0 + adr1) + adr2) + adr3, m0 = fs0[ri[inodekey(m3)]].nlink, m1 = fs0[ri[inodekey(m3)]].nsubdirs, m2 = fs0[ri[inodekey(m3)]].size, nd = inodenode(inodekey(n), md, true, 1, 0, 0), nd0 = dentrynode(dentrykey(m3, str), n), nd1 = inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1), p_inode = mkinode(m3, md0, true, fs0[ri[inodekey(m3)]].nlink, fs0[ri[inodekey(m3)]].nsubdirs, fs0[ri[inodekey(m3)]].size), ri0 = ri, ro = orphans(fs1, ri), ro0 = orphans(fs0, ri), fs0[ri[inodekey(m3)]].inode?, fo.inodes?, orphans(fs1, ri).inodes?, afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), file-node-cons(fs1, ri), log-cons(log0, fs1), new(adr1 ' + (adr2 ' + adr3), fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri[inodekey(m3)] ∈ fs1, ri[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri, asynced → boolvar0, m ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs1, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs0[ri[inodekey(m3)]].trunc? ∨ fs0[ri[inodekey(m3)]].inode? ⊦ [aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, orphans(fs0, ri), fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(p_inode.ino, dent.name), adr2, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(n), adr3, fi, orphans(fs0, ri0), fo, fs, log, boolvar; ri); dent := mkdentry(dent.name, n); p_inode := mkinode (p_inode.ino, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).meta, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).directory, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).nlink, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).nsubdirs, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).size); c_inode := mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size)] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨old_dent := negdentry(str); p_inode0 := mkinode(m3, md0, true, m0, m1, m2); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ err = err0)), n = 0, dups(adr1 ' + adr2 ' + adr3 '), dentrykey(m3, str) ∈ ri, inodekey(n) ∈ fo, inodekey(n) ∈ ri, m = 0 ∧ m3 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
fs1[ri[inodekey(m3)]] = inodenode(key, md1, true, m, m4, m5), dirs = abs-dirs(fs1, ri), files = abs-files(fs1, ri), ri0 = ri, ro0 = orphans(fs1, ri), adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, n ≠ 0, fo.inodes?, orphans(fs1, ri).inodes?, afs-cons(abs-dirs(fs1, ri), abs-files(fs1, ri)), file-node-cons(fs1, ri), log-cons(log0, fs1), orphans-cons(fs1, ri, orphans(fs1, ri)), replay-cons-strong(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs1, ri, orphans(fs1, ri), fi, fo, log0), ri[inodekey(m3)] ∈ fs1, inodekey(m3) ∈ ri, ¬ dentrykey(m3, str) ∈ ri, ¬ inodekey(n) ∈ fo, ¬ inodekey(n) ∈ ri, ¬ adr1 ∈ fs1, ¬ adr2 ∈ fs1, ¬ adr3 ∈ fs1, asynced → boolvar0, m ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs1, ri)) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [aubifs_core_index_store# (inodekey (mkinode (m3, md0, true, inodenode(key, md1, true, m, m4, m5).nlink, inodenode(key, md1, true, m, m4, m5).nsubdirs, inodenode(key, md1, true, m, m4, m5).size) .ino), adr1, fi, orphans(fs1, ri), fo, fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (dentrykey (mkinode (m3, md0, true, inodenode(key, md1, true, m, m4, m5).nlink, inodenode(key, md1, true, m, m4, m5).nsubdirs, inodenode(key, md1, true, m, m4, m5).size) .ino, str), adr2, fi, orphans(fs1, ri0), fo, fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (inodekey(n), adr3, fi, orphans(fs1, ri0), fo, fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); dent := mkdentry(str, n); p_inode := mkinode (mkinode (m3, md0, true, inodenode(key, md1, true, m, m4, m5).nlink, inodenode(key, md1, true, m, m4, m5).nsubdirs, inodenode(key, md1, true, m, m4, m5).size) .ino, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).meta, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).directory, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).nlink, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).nsubdirs, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1).size); c_inode := mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size)] ( ubifs-cons (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans-cons (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri, ro0) ∧ ri-inj(ri) ∧ log-cons (log0, fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]) ∧ m3 ≠ 0 → ⟨old_dent := negdentry(str); p_inode0 := mkinode (m3, md0, true, inodenode(key, md1, true, m, m4, m5).nlink, inodenode(key, md1, true, m, m4, m5).nsubdirs, inodenode(key, md1, true, m, m4, m5).size); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ files = abs-files (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri) ∧ orphans (abs-dirs (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri), abs-files (fs1[adr1, inodenode(inodekey(m3), md0, true, m, m4 + 1, m5 + 1)][adr2, dentrynode(dentrykey(m3, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = old_dent ∧ ESUCCESS = err0)), m = 0 ∧ m3 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr0, nd] ↔ adr = adr0 ∨ adr ∈ fs; (ws)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ negdentry(str).name = str; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)