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Proof step 8 from proof inv-rmdir (previous step)

c_inode.ino = fs[ri[dentrykey(p_inode.ino, str)]].ino, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nlink = 1, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, c_inode.size = fs[ri[inodekey(c_inode.ino)]].size, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, 1 = fs[ri[inodekey(c_inode.ino)]].nlink, dent = mkdentry(str, c_inode.ino), dentrykeys(inodekey(c_inode.ino), ri) = ∅, ino = c_inode.ino, links(c_inode.ino, fs, ri) = ∅ ++ dentrykey(p_inode.ino, str), c_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rmdir(p_inode, c_inode, dent, fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(p_inode.ino) ∈ ri, inodekey(c_inode.ino) ∈ ri, dentrykey(p_inode.ino, str) ∈ ri, 1 ≤ p_inode.size, 1 ≤ p_inode.nsubdirs, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO ⊦ ⟪key1 := inodekey(p_inode.ino); key0 := dentrykey(p_inode.ino, dent.name); key := inodekey(c_inode.ino); nd1 := inodenode(key1, p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1); nd0 := dentrynode(key0, 0); nd := inodenode(key, c_inode.meta, c_inode.directory, c_inode.nlink - 1, c_inode.nsubdirs, c_inode.size); aubifs_core_journal_add3#(nd1, nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(key1, adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(key0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(dent.name); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.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)), c_inode.ino = ROOT_INO, p_inode.nsubdirs = 0, p_inode.size = 0, inodekey(p_inode.ino) ∈ ro, inodekey(c_inode.ino) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
c_inode.ino = fs[ri[dentrykey(p_inode.ino, str)]].ino, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nlink = 1, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, c_inode.size = fs[ri[inodekey(c_inode.ino)]].size, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, 1 = fs[ri[inodekey(c_inode.ino)]].nlink, dentrykeys(inodekey(c_inode.ino), ri) = ∅, links(c_inode.ino, fs, ri) = ∅ ++ dentrykey(p_inode.ino, str), c_inode.ino ≠ ROOT_INO, p_inode.nsubdirs ≠ 0, p_inode.size ≠ 0, c_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(p_inode.ino) ∈ ri, inodekey(c_inode.ino) ∈ ri, dentrykey(p_inode.ino, str) ∈ ri, 1 ≤ p_inode.size, 1 ≤ p_inode.nsubdirs, ¬ inodekey(p_inode.ino) ∈ ro, ¬ inodekey(c_inode.ino) ∈ ro, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO ⊦ ⟪key1 := inodekey(p_inode.ino); key0 := dentrykey(p_inode.ino, str); key := inodekey(c_inode.ino); nd1 := inodenode(key1, p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs - 1, p_inode.size - 1); nd0 := dentrynode(key0, 0); nd := inodenode(key, c_inode.meta, c_inode.directory, 0, c_inode.nsubdirs, c_inode.size); aubifs_core_journal_add3#(nd1, nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(key1, adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_remove#(key0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode0 := mkinode(c_inode.ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.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))

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ valid-dir-inode(inode, fs, ri) ↔ valid-dir-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.size = fs[ri[inodekey(inode.ino)]].size; (s)% ⊦ {key} = ∅ ++ key; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ valid-dentry(ino, dent, fs, ri, ro) ↔ dent.dentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ valid-ino(dent.ino, fs, ri) ∧ dentrykey(ino, dent.name) ∈ ri ∧ fs[ri[dentrykey(ino, dent.name)]].ino = dent.ino; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ pre-rmdir(p_inode, c_inode, dent, fs, ri, ro) ↔ dent.ino ≠ ROOT_INO ∧ valid-dentry(p_inode.ino, dent, fs, ri, ro) ∧ fs[ri[inodekey(dent.ino)]].nlink = 1 ∧ links(dent.ino, fs, ri) = {dentrykey(p_inode.ino, dent.name)} ∧ dentrykeys(inodekey(dent.ino), ri) = ∅ ∧ ¬ inodekey(dent.ino) ∈ ro ∧ valid-dir-inode(p_inode, fs, ri) ∧ valid-dir-inode(c_inode, fs, ri) ∧ c_inode.ino = dent.ino ∧ p_inode.nsubdirs ≥ 1 ∧ p_inode.size ≥ 1; (s)