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Proof step 54 from proof inv-rmdir (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].inode?, fs0[ri0[inodekey(m0)]].inode?, ro.inodes?, fo.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(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, ri0[key] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m0)]].size, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[dentrykey(m0, str)]].ino = 0, fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, inodekey(m0) = key, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) = key, key = dentrykey(m0, str), m0 = 0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ key.ino ≠ fs0[ri0[dentrykey(m0, str)]].ino ∧ ¬ inodekey(key.ino) ∈ ro ∧ fs0[ri0[key]].ino ≠ fs0[ri0[dentrykey(m0, str)]].ino ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ (adr3 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])] ) ) ) .directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ (key.ino = fs0[ri0[dentrykey(m0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 55:
1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nlink, dentrykeys(inodekey(fs0[ri0[dentrykey(m0, str)]].ino), ri0) = ∅, links(fs0[ri0[dentrykey(m0, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m0, str), fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].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, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, key ∈ ri0, 1 ≤ fs0[ri0[inodekey(m0)]].nsubdirs, 1 ≤ fs0[ri0[inodekey(m0)]].size, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ 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? ∧ key.ino ≠ 0, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ fs0[ri0[dentrykey(m0, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m0, str)]].ino = 0, key.ino = 0, fs0[ri0[inodekey(m0)]].nsubdirs = 0, fs0[ri0[inodekey(m0)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) = key, inodekey(m0) = key, key = dentrykey(m0, str), m0 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(fs0[ri0[dentrykey(m0, str)]].ino) ∈ ro, ( key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ key.ino ≠ fs0[ri0[dentrykey(m0, str)]].ino ∧ ¬ inodekey(key.ino) ∈ ro ∧ fs0[ri0[key]].ino ≠ fs0[ri0[dentrykey(m0, str)]].ino ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ (adr3 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])] ) ) ) .directory) ∧ ( key.data? → fs0[ri0[key]].data? ∧ (key.ino = fs0[ri0[dentrykey(m0, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m0, str)]].ino), md, true, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].nsubdirs, fs0[ri0[inodekey(fs0[ri0[dentrykey(m0, str)]].ino)]].size) ;(adr2 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m0, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs - 1, fs0[ri0[inodekey(m0)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m0, str)]].ino = key.ino ⊃ adr3;(m0 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE)

Rule argument

fma: key.ino = 0

Additional information

Used simplifier rules: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s) Used formulas: key.ino = 0