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Proof step 162 from proof inv-link (previous step)

c_inode.ino = fs[ri[dentrykey(ino, 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, new_dent = negdentry(str0), old_dent = mkdentry(str, fs[ri[dentrykey(ino, str)]].ino), fs[ri[dentrykey(ino, str)]].dentry?, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(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), ri[dentrykey(ino, str)] ∈ fs, inodekey(ino) ∈ ri, inodekey(c_inode.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino, str) ∈ ri, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ c_inode.directory, fs[ri[inodekey(c_inode.ino)]].directory, pre-link(p_inode, c_inode, old_dent, new_dent, fs, ri, ro), inodekey(c_inode.ino) ∈ ro, dentrykey(p_inode.ino, str0) ∈ ri, inodekey(p_inode.ino) ∈ ro, inodekey(ino) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 163:
c_inode.ino = fs[ri[dentrykey(ino, 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(ino, str)]].dentry?, p_inode.directory, fs[ri[inodekey(p_inode.ino)]].directory, fs[ri[inodekey(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), ri[dentrykey(ino, str)] ∈ fs, inodekey(ino) ∈ ri, inodekey(c_inode.ino) ∈ ri, inodekey(p_inode.ino) ∈ ri, dentrykey(ino, str) ∈ ri, p_inode.nlink ≠ 0 ∨ p_inode.ino = ROOT_INO, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ 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(ino) ∈ ro, ∃ ino0. inodekey(ino0) ∈ ri ∧ (fs[ri[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO) ∧ ¬ inodekey(ino0) ∈ ro ∧ dentrykey(ino0, str) ∈ ri ∧ fs[ri[dentrykey(ino0, str)]].ino = c_inode.ino

Rule argument

Additional information

Used simplifier rules: ⊦ 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)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ 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)