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Proof step 67 from proof inv-unlink (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), key.dentry?, fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[key] ∈ fs0, dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, key ∈ ri0, inodekey(key.ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, key.data? → fs0[ri0[key]].data? ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory, key.inode? → fs0[ri0[key]].inode?, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, key.ino = 0, key.ino = fs0[ri0[dentrykey(m1, str)]].ino, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key, inodekey(m1) = key, key = dentrykey(m1, str), m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro, fs0[ri0[key]].dentry? ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ fs0[ri0[key]].ino ≠ fs0[ri0[dentrykey(m1, str)]].ino ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ (adr3 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])] ) ) ) .directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[dentrykey(ino, str0)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[dentrykey(ino, str0)] ∈ fs0, dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, dentrykey(ino, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino, str0)]].ino) ∈ ri0, inodekey(ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, dentrykey(ino, str0) = dentrykey(m1, str), ino = 0, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro, inodekey(fs0[ri0[dentrykey(ino, str0)]].ino) ∈ ro, inodekey(ino) ∈ ro, fs0[ri0[dentrykey(ino, str0)]].ino ≠ fs0[ri0[dentrykey(m1, str)]].ino ∧ (adr3 = (m1 = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (m1 = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (m1 = ino ⊃ adr1;ri0[inodekey(ino)]) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(m1 = ino ⊃ adr1;ri0[inodekey(ino)])] ) ) ) .directory

Rule argument

Additional information

Used simplifier rules: elim-dentry: ⊦ key.dentry? ↔ (∃ ino, str. key = dentrykey(ino, str));%dentry-ubifs-cons: ⊦ dentrykey(ino, str) ∈ ri ∧ ri[dentrykey(ino, str)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[dentrykey(ino, str)]].dentry?;%ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv% ⊦ ¬ dentrykey(m, str).inode?; (s)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ dentrykey(m, str).ino = m; (s)