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Proof step 27 from proof inv-rmdir (previous step)

1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nlink, adr4 = adr5, dentrykeys(inodekey(fs0[ri[dentrykey(m0, str)]].ino), ri) = ∅, err = ESUCCESS, fs = fs0[adr1, nd1][adr2, nd0][adr3, nd], links(fs0[ri[dentrykey(m0, str)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str), log = ((log0 + adr1) + adr2) + adr3, m = fs0[ri[dentrykey(m0, str)]].ino, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs0[ri[inodekey(m0)]].nlink, m4 = fs0[ri[inodekey(m0)]].nsubdirs, m5 = fs0[ri[inodekey(m0)]].size, nd = inodenode(inodekey(m), md, true, 0, m1, m2), nd0 = dentrynode(dentrykey(m0, str), 0), nd1 = inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1), fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].directory, fs0[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(m0) ∈ ri, 1 ≤ fs0[ri[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri[inodekey(m0)]].size, m5 ≥ 1, m4 ≥ 1, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).size)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro)), fs0[ri[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri[inodekey(m0)]].nsubdirs = 0, fs0[ri[inodekey(m0)]].size = 0, dups(adr1 ' + adr2 ' + adr3 '), inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ro, inodekey(m0) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri[dentrykey(m0, str)]].ino), ri) = ∅, fs = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs - 1, fs0[ri[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size) ], links(fs0[ri[dentrykey(m0, str)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str), m = fs0[ri[dentrykey(m0, str)]].ino, m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].size, m3 = fs0[ri[inodekey(m0)]].nlink, m4 = fs0[ri[inodekey(m0)]].nsubdirs, m5 = fs0[ri[inodekey(m0)]].size, fs0[ri[dentrykey(m0, str)]].ino ≠ ROOT_INO, fs0[ri[dentrykey(m0, str)]].ino ≠ 0, fs0[ri[inodekey(m0)]].nsubdirs ≠ 0, fs0[ri[inodekey(m0)]].size ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, m0 ≠ 0, fs0[ri[inodekey(m0)]].directory, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), inodekey(m0) ∈ ri, dentrykey(m0, str) ∈ ri, inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ri, 1 ≤ fs0[ri[inodekey(m0)]].size, 1 ≤ fs0[ri[inodekey(m0)]].nsubdirs, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m0) ∈ ro, ¬ inodekey(fs0[ri[dentrykey(m0, str)]].ino) ∈ ro, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_index_store#(inodekey(m0), adr1, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_remove#(dentrykey(m0, str), fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).meta, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).directory, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nlink, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).nsubdirs, inodenode(inodekey(m0), md0, true, m3, m4 - 1, m5 - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(m), md, true, 0, m1, m2).meta, inodenode(inodekey(m), md, true, 0, m1, m2).directory, inodenode(inodekey(m), md, true, 0, m1, m2).nlink, inodenode(inodekey(m), md, true, 0, m1, m2).nsubdirs, inodenode(inodekey(m), md, true, 0, m1, m2).size)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]% ⊦ 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)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (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)% ⊦ n ≥ m ↔ m ≤ n; (s)