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Proof step 10 from proof inv-link (previous step)

c_inode.ino = fs[ri[dentrykey(ino0, str)]].ino, c_inode.nlink = fs[ri[inodekey(c_inode.ino)]].nlink, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, ino = c_inode.ino, new_dent = negdentry(str0), old_dent = mkdentry(str, fs[ri[dentrykey(ino0, str)]].ino), fs[ri[dentrykey(ino0, str)]].dentry?, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(ino0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-link(p_inode, c_inode, old_dent, new_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), ri[dentrykey(ino0, str)] ∈ fs, inodekey(ino0) ∈ ri, inodekey(c_inode.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino0, str) ∈ ri, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO, fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪key1 := inodekey(p_inode.ino); key0 := dentrykey(p_inode.ino, new_dent.name); key := inodekey(ino); nd1 := inodenode(key1, p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1); nd0 := dentrynode(key0, ino); 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_store#(key0, adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(new_dent.name, ino); 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.directory, fs[ri[inodekey(c_inode.ino)]].directory, inodekey(c_inode.ino) ∈ ro, dentrykey(p_inode.ino, str0) ∈ ri, inodekey(p_inode.ino) ∈ ro, inodekey(ino0) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
fs[ri[dentrykey(ino, str)]].ino = c_inode.ino, c_inode.ino = fs[ri[dentrykey(ino0, str)]].ino, c_inode.nlink = fs[ri[inodekey(c_inode.ino)]].nlink, p_inode.nlink = fs[ri[inodekey(p_inode.ino)]].nlink, c_inode.nsubdirs = fs[ri[inodekey(c_inode.ino)]].nsubdirs, p_inode.nsubdirs = fs[ri[inodekey(p_inode.ino)]].nsubdirs, p_inode.size = fs[ri[inodekey(p_inode.ino)]].size, fs[ri[dentrykey(ino0, str)]].dentry?, fs[ri[inodekey(ino)]].directory, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(ino0)]].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(ino0) ∈ ri, dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, ri[dentrykey(ino0, str)] ∈ fs, inodekey(c_inode.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino0, str) ∈ ri, ¬ c_inode.directory, ¬ fs[ri[inodekey(c_inode.ino)]].directory, ¬ inodekey(ino) ∈ ro, ¬ inodekey(c_inode.ino) ∈ ro, ¬ dentrykey(p_inode.ino, str0) ∈ ri, ¬ inodekey(p_inode.ino) ∈ ro, ¬ inodekey(ino0) ∈ ro, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO, fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪key1 := inodekey(p_inode.ino); key0 := dentrykey(p_inode.ino, str0); key := inodekey(c_inode.ino); nd1 := inodenode(key1, p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1); nd0 := dentrynode(key0, c_inode.ino); 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_store#(key0, adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(str0, c_inode.ino); 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: ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%⊦ valid-file-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-file-inode(inode, fs, ri) ↔ valid-file-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; (s)%⊦ 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)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (s)%⊦ valid-negdentry(ino, dent, fs, ri, ro) ↔ dent.negdentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ ¬ dentrykey(ino, dent.name) ∈ ri; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)% ⊦ mkdentry(str, m).ino = m; (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)%⊦ valid-dentry(dent, fs, ri, ro) ↔ (∃ ino. valid-dentry(ino, dent, fs, ri, ro)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, fs, ri, ro) ↔ ( valid-dentry(old_dent, fs, ri, ro) ∧ valid-negdentry(p_inode.ino, new_dent, fs, ri, ro) ∧ ¬ inodekey(old_dent.ino) ∈ ro) ∧ valid-dir-inode(p_inode, fs, ri) ∧ valid-file-inode(c_inode, fs, ri) ∧ c_inode.ino = old_dent.ino; (s)