[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 31 from proof inv-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, adr = adr1, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, fs = fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], key = inodekey(m0), links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', m = fs0[ri0[dentrykey(m0, str)]].ino, m1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, m2 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size, m3 = fs0[ri0[inodekey(m0)]].nlink, m4 = fs0[ri0[inodekey(m0)]].nsubdirs, m5 = fs0[ri0[inodekey(m0)]].size, ri = ri0[key, adr], fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, fs0[ri0[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(m0) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m0)]].size, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪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)), fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m0, str)]].ino = 0, fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), ri = ri0[inodekey(m0), adr1], fs0[ri0[dentrykey(m0, str)]].ino ≠ 0, fs0[ri0[dentrykey(m0, str)]].ino ≠ ROOT_INO, fs0[ri0[inodekey(m0)]].nsubdirs ≠ 0, fs0[ri0[inodekey(m0)]].size ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m0 ≠ 0, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m0, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, inodekey(m0) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].size, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, ¬ inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro, ¬ inodekey(m0) ∈ ro, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ ⟪aubifs_core_index_remove# (dentrykey(m0, str), fi, ro, fo, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), adr3, fi, ro, fo, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_orphans_insert# (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri, fi, fo, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1)] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ro); dent := negdentry(str); p_inode0 := mkinode (m0, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1).meta, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) .directory, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1).nlink, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1).nsubdirs, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1).size); c_inode0 := mkinode (fs0[ri0[dentrykey(m0, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) .meta, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) .directory, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) .size)⟫ ( ubifs-cons (fs0 [adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0 [adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0 [adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ri) ∧ orphans-cons (fs0 [adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ] [adr2, dentrynode(dentrykey(m0, str), 0) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ], ri, ro))

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]