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Proof step 52 from proof refine-rename-new-reparent (previous step)

m11 + 1 = fs0[ri[inodekey(m3)]].size, n0 + (boolvar1 ⊃ 1;0) = fs0[ri[inodekey(m3)]].nsubdirs, boolvar2 ↔ boolvar, adr5 = adr, adr6 = adr8, adr7 = adr2, dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs0[adr1, nd2][adr2, nd1][adr3, nd0][adr4, nd], log = (((log0 + adr1) + adr2) + adr3) + adr4, m = fs0[ri[dentrykey(m3, str)]].ino, m10 = fs0[ri[inodekey(m7)]].size, m4 = fs0[ri[inodekey(m3)]].nlink, m8 = fs0[ri[inodekey(m7)]].nlink, m9 = fs0[ri[inodekey(m7)]].nsubdirs, nd = inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1), nd0 = inodenode(inodekey(m3), md0, true, m4, n0, m11), nd1 = dentrynode(dentrykey(m7, str0), old_dent.ino), nd2 = dentrynode(dentrykey(m3, old_dent.name), 0), new_dent = negdentry(str0), new_parent_inode = mkinode(m7, md1, true, m8, m9, m10), old_dent = mkdentry(str, fs0[ri[dentrykey(m3, str)]].ino), old_parent_inode = mkinode(m3, md0, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1), ro = orphans(fs0, ri), ro0 = orphans(fs0, ri), old_dent.dentry?, fs0[ri[inodekey(m7)]].directory, fs0[ri[inodekey(m3)]].directory, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m7) ∈ ri, dentrykey(m3, str) ∈ ri, inodekey(fs0[ri[dentrykey(m3, str)]].ino) ∈ ri, inodekey(m3) ∈ ri, boolvar3 → boolvar0, fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].size, links(m7, abs-dirs(fs0, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs0, ri)) ≠ ∅ ∨ m3 = ROOT_INO, fs0[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, fs0[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO ⊦ [aubifs_core_index_remove#(dentrykey(m3, old_dent.name), fi, ro0, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(dentrykey(m7, new_dent.name), adr7, fi, ro0, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(inodekey(m3), adr3, fi, ro0, fo, fs, log, boolvar2; ri); aubifs_core_index_store#(inodekey(m7), adr4, fi, ro0, fo, fs, log, boolvar2; ri); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode := mkinode (old_parent_inode.ino, inodenode(inodekey(m3), md0, true, m4, n0, m11).meta, inodenode(inodekey(m3), md0, true, m4, n0, m11).directory, inodenode(inodekey(m3), md0, true, m4, n0, m11).nlink, inodenode(inodekey(m3), md0, true, m4, n0, m11).nsubdirs, inodenode(inodekey(m3), md0, true, m4, n0, m11).size); new_parent_inode := mkinode (new_parent_inode.ino, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).meta, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).directory, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).nlink, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).nsubdirs, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).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_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode0 := new_dent_inode; old_dent0 := mkdentry(str, m); old_dent1 := negdentry(str0); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); old_inode := mkinode(m3, md0, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1); new_inode := mkinode(m7, md1, true, m8, m9, m10); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)), m3 = m7, dups(adr1 ' + adr2 ' + adr3 ' + adr4 '), dentrykey(m7, str0) ∈ ri, fs0[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO, fs0[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
n0 + (boolvar1 ⊃ 1;0) = fs0[ri[inodekey(m3)]].nsubdirs, m11 + 1 = fs0[ri[inodekey(m3)]].size, dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs = fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m7, str0), fs0[ri[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri[inodekey(m3)]].nlink, n0, m11) ] [adr4, inodenode(inodekey(m7), md1, true, fs0[ri[inodekey(m7)]].nlink, fs0[ri[inodekey(m7)]].nsubdirs + (boolvar1 ⊃ 1;0), fs0[ri[inodekey(m7)]].size + 1) ], m = fs0[ri[dentrykey(m3, str)]].ino, m10 = fs0[ri[inodekey(m7)]].size, m4 = fs0[ri[inodekey(m3)]].nlink, m8 = fs0[ri[inodekey(m7)]].nlink, m9 = fs0[ri[inodekey(m7)]].nsubdirs, old_dent = mkdentry(str, fs0[ri[dentrykey(m3, str)]].ino), ro = orphans(fs0, ri), adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m3 ≠ m7, fs0[ri[inodekey(m3)]].directory, fs0[ri[inodekey(m7)]].directory, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m3) ∈ ri, inodekey(fs0[ri[dentrykey(m3, str)]].ino) ∈ ri, dentrykey(m3, str) ∈ ri, inodekey(m7) ∈ ri, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ dentrykey(m7, str0) ∈ ri, boolvar3 → boolvar0, fs0[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri[inodekey(m7)]].nlink ≠ 0 ∨ m7 = ROOT_INO, links(m3, abs-dirs(fs0, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m7, abs-dirs(fs0, ri)) ≠ ∅ ∨ m7 = ROOT_INO, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].size, fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri[inodekey(fs0[ri[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ [aubifs_core_index_remove# (dentrykey(m3, old_dent.name), fi, orphans(fs0, ri), fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar2; ri); aubifs_core_index_store#(dentrykey(m7, str0), adr2, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar2; ri); aubifs_core_index_store#(inodekey(m3), adr3, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar2; ri); aubifs_core_index_store#(inodekey(m7), adr4, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar2; ri); new_dent := mkdentry(str0, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode := mkinode (m3, inodenode(inodekey(m3), md0, true, m4, n0, m11).meta, inodenode(inodekey(m3), md0, true, m4, n0, m11).directory, inodenode(inodekey(m3), md0, true, m4, n0, m11).nlink, inodenode(inodekey(m3), md0, true, m4, n0, m11).nsubdirs, inodenode(inodekey(m3), md0, true, m4, n0, m11).size); new_parent_inode := mkinode (m7, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).meta, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).directory, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).nlink, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).nsubdirs, inodenode(inodekey(m7), md1, true, m8, m9 + (boolvar1 ⊃ 1;0), m10 + 1).size)] ( ubifs-cons(fs, ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ replay-cons-strong(fs, ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log0, fs) ∧ adr1 ∈ fs ∧ node-cons(fs[adr1].key, fs[adr1]) ∧ adr2 ∈ fs ∧ node-cons(fs[adr2].key, fs[adr2]) ∧ adr3 ∈ fs ∧ node-cons(fs[adr3].key, fs[adr3]) ∧ adr4 ∈ fs ∧ node-cons(fs[adr4].key, fs[adr4]) → ⟨old_dent_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode0 := new_dent_inode; old_dent0 := mkdentry(str, m); old_dent1 := negdentry(str0); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); old_inode := mkinode(m3, md0, true, m4, n0 + (boolvar1 ⊃ 1;0), m11 + 1); new_inode := mkinode(m7, md1, true, m8, m9, m10); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), fs0[ri[inodekey(m7)]].nlink = 0 ∧ m7 ≠ ROOT_INO, fs0[ri[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (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)% ⊦ mkdentry(str, m).name = str; (s)