[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 33 from proof inv-rename-new-keep-parent (previous step)

fs0[ri[dentrykey(m, str)]] = dentrynode(key, m0), adr4 = adr5, err = ESUCCESS, fs = fs0[adr1, nd1][adr2, nd0][adr3, nd], log = ((log0 + adr1) + adr2) + adr3, m4 = fs0[ri[inodekey(m)]].nlink, m5 = fs0[ri[inodekey(m)]].nsubdirs, m6 = fs0[ri[inodekey(m)]].size, nd = inodenode(inodekey(m), md, true, m4, m5, m6), nd0 = dentrynode(dentrykey(m, str0), mkdentry(str, m0).ino), nd1 = dentrynode(dentrykey(m, str), 0), mkdentry(str, m0).dentry?, fs0[ri[inodekey(m)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + (adr2 ' + adr3), fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), dentrykey(m, str) ∈ ri, inodekey(m0) ∈ ri, inodekey(m) ∈ ri, ri[dentrykey(m, str)] ∈ fs0, 1 ≤ fs0[ri[inodekey(m)]].size, boolvar2 → 1 ≤ fs0[ri[inodekey(m)]].nsubdirs, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri[inodekey(m0)]].directory ∧ ¬ boolvar2 ∧ m1 = fs0[ri[inodekey(m0)]].nlink ∧ m2 = fs0[ri[inodekey(m0)]].nsubdirs ∨ fs0[ri[inodekey(m0)]].directory ∧ boolvar2 ∧ m1 = fs0[ri[inodekey(m0)]].nlink ∧ m2 = fs0[ri[inodekey(m0)]].nsubdirs ∧ m3 = fs0[ri[inodekey(m0)]].size ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(str0, mkdentry(str, m0).ino); old_dent := negdentry(str); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m4, m5, m6).meta, inodenode(inodekey(m), md, true, m4, m5, m6).directory, inodenode(inodekey(m), md, true, m4, m5, m6).nlink, inodenode(inodekey(m), md, true, m4, m5, m6).nsubdirs, inodenode(inodekey(m), md, true, m4, m5, m6).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[inodekey(m)]].size = 0, dups(adr1 ' + adr2 ' + adr3 '), inodekey(m) ∈ ro, dentrykey(m, str0) ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
fs0[ri[dentrykey(m, str)]] = dentrynode(key, m0), fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m0)] [adr3, inodenode(inodekey(m), md, true, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, fs0[ri[inodekey(m)]].size) ], m4 = fs0[ri[inodekey(m)]].nlink, m5 = fs0[ri[inodekey(m)]].nsubdirs, m6 = fs0[ri[inodekey(m)]].size, fs0[ri[inodekey(m)]].size ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr2 ≠ adr3, fs0[ri[inodekey(m)]].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-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs0[ri[inodekey(m)]].size, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ dentrykey(m, str0) ∈ ri, ¬ inodekey(m) ∈ ro, boolvar2 → 1 ≤ fs0[ri[inodekey(m)]].nsubdirs, ¬ fs0[ri[inodekey(m0)]].directory ∧ ¬ boolvar2 ∧ m1 = fs0[ri[inodekey(m0)]].nlink ∧ m2 = fs0[ri[inodekey(m0)]].nsubdirs ∨ fs0[ri[inodekey(m0)]].directory ∧ boolvar2 ∧ m1 = fs0[ri[inodekey(m0)]].nlink ∧ m2 = fs0[ri[inodekey(m0)]].nsubdirs ∧ m3 = fs0[ri[inodekey(m0)]].size, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, 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); new_dent := mkdentry(str0, mkdentry(str, m0).ino); old_dent := negdentry(str); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m4, m5, m6).meta, inodenode(inodekey(m), md, true, m4, m5, m6).directory, inodenode(inodekey(m), md, true, m4, m5, m6).nlink, inodenode(inodekey(m), md, true, m4, m5, m6).nsubdirs, inodenode(inodekey(m), md, true, m4, m5, m6).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: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ 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)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ 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)% ⊦ mkdentry(str, m).ino = m; (s)