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Proof step 96 from proof inv-rmdir (previous step)

fs0[ri0[inodekey(m0)]].nsubdirs = m + 1, fs0[ri0[inodekey(m0)]].size = m1 + 1, 1 = fs0[ri0[inodekey(m2)]].nlink, fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m2), dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m0, str), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fs0[ri0[dentrykey(m0, str)]].dentry?, fs0[ri0[inodekey(m2)]].directory, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m0)]].inode?, fs0[ri0[inodekey(m2)]].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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m0, str) ∈ ri0, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, m2 = ROOT_INO, m2 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m2) ∈ ro, replay-safe (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] ∧ ¬ adr3 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] -- dentrykey(m0, str) ∧ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] -- dentrykey(m0, str) -- inodekey(m2) = (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3] ⊖ (ro ++ inodekey(m2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
fs0[ri0[inodekey(m0)]].nsubdirs = m + 1, fs0[ri0[inodekey(m0)]].size = m1 + 1, 1 = fs0[ri0[inodekey(m2)]].nlink, fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m2), dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m0, str), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m2)]].directory, fs0[ri0[inodekey(m2)]].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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m0, str) ∈ ri0, inodekey(m2) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, m2 = 0, m2 = ROOT_INO, inodekey(m2) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, replay-safe (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] ∧ ¬ adr3 ∈ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] -- dentrykey(m0, str) ∧ replay-log (log0, fs0[adr1, inodenode(inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, m, m1)][adr2, dentrynode(dentrykey(m0, str), 0)] [adr3, inodenode(inodekey(m2), md, true, 0, fs0[ri0[inodekey(m2)]].nsubdirs, fs0[ri0[inodekey(m2)]].size) ], fi ⊖ fo) [inodekey(m0), adr1 ] -- dentrykey(m0, str) -- inodekey(m2) = (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3] ⊖ (ro ++ inodekey(m2))

Rule argument

Additional information

Used simplifier rules: ⊦ #(∅ ++ key) = 1; (s)% ⊦ dentrynode(key, m).dentry?; (s)%one-size: ⊦ ks = ∅ ++ key → # ks = 1; (forward) from specification set-basic[node-index]