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Proof step 92 from proof refine-rename-overwrite-reparent-file (previous step)

m12 + 1 = fs0[ri0[inodekey(m0)]].nlink, nd.nlink = 0, boolvar ↔ boolvar1, 0 = fs0[ri0[inodekey(m)]].nsubdirs, 0 = fs0[ri0[inodekey(m0)]].nsubdirs, fs0[ri0[inodekey(m4)]] = inodenode(key2, md4, true, m6, m7, m8), fs0[ri0[dentrykey(m4, str0)]] = dentrynode(key0, m0), fs0[ri0[dentrykey(m9, str)]] = dentrynode(key3, m), fs0[ri0[inodekey(m9)]] = inodenode(key1, md3, true, m1, m3, m14 + 1), adr = adr5, fs = fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], fs1 = fs0[adr1, dentrynode(dentrykey(m9, str), 0)][adr2, dentrynode(dentrykey(m4, str0), m)][adr3, inodenode(inodekey(m9), md2, true, m1, m3, m14)] [adr4, inodenode(inodekey(m4), md1, true, m6, m7, m8) ] [adr5, inodenode(inodekey(m0), md0, false, m12, 0, m5) ], key = inodekey(mkdentry(str0, m0).ino), log = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', log1 = ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', nd = inodenode(inodekey(mkdentry(str0, m0).ino), md0, false, m12, 0, m5), new_dent = mkdentry(str0, m0), ri = ri1[key, adr], ri1 = (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3][inodekey(m4), adr4], ro = orphans(fs0, ri0), ro0 = orphans(fs0, ri0), mkdentry(str0, m0).dentry?, nd.inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), key-cons(key, fs1[adr]), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m9, str)] ∈ fs0, ri0[inodekey(m9)] ∈ fs0, ri0[inodekey(m4)] ∈ fs0, ri0[dentrykey(m4, str0)] ∈ fs0, inodekey(m4) ∈ ri0, inodekey(m9) ∈ ri0, dentrykey(m4, str0) ∈ ri0, inodekey(m0) ∈ ri0, dentrykey(m9, str) ∈ ri0, inodekey(m) ∈ ri0, adr ∈ fs1, boolvar2 → boolvar0, m12 = 0 → links(m0, fs0, ri0) = ∅ ++ dentrykey(m4, str0), ¬ adr ∈ ri1 → adr ∈ fs1 → adr ∈ fs1, m6 ≠ 0 ∨ m4 = ROOT_INO, m1 ≠ 0 ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m4 = ROOT_INO, links(m9, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m9 = ROOT_INO ⊦ [aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar1; ro0); new_dent := mkdentry(new_dent.name, mkdentry(str, m).ino); old_dent := negdentry(str); old_parent_inode := mkinode (m9, inodenode(inodekey(m9), md2, true, m1, m3, m14).meta, inodenode(inodekey(m9), md2, true, m1, m3, m14).directory, inodenode(inodekey(m9), md2, true, m1, m3, m14).nlink, inodenode(inodekey(m9), md2, true, m1, m3, m14).nsubdirs, inodenode(inodekey(m9), md2, true, m1, m3, m14).size); new_child_inode := mkinode(m0, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.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) ∧ ro0.inodes? → ⟨old_dent_inode0 := mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m0); old_dent_inode := mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2); new_dent_inode := mkinode(m0, md0, false, m12 + 1, 0, m5); new_inode := mkinode(m4, md1, true, m6, m7, m8); old_inode := mkinode(m9, md2, true, m1, m3, m14 + 1); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar2)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar2 → boolvar1) ∧ old_parent_inode = old_inode ∧ mkinode(m4, md1, true, m6, m7, m8) = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m0 = 0, m0 = ROOT_INO, m4 = 0, m9 = 0, m9 = m4, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, adr ∈ ri1, adr3 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m9, str), adr4 ∈ (ri0 -- dentrykey(m9, str))[dentrykey(m4, str0), adr2][inodekey(m9), adr3], m1 = 0 ∧ m9 ≠ ROOT_INO, m6 = 0 ∧ m4 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ 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)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (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)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ mkdentry(str, m).ino = m; (s)