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Proof step 216 from proof refine-rmdir (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key2, md6, true, 1, m12 + 1, m10 + 1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m), abs-children(m, fs0, ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m, str), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, asynced0 → boolvar0, ∀ key. key ∈ dentrykeys(inodekey(m), ri0) ↔ key ∈ ∅ ⊦ # links(m, abs-dirs(fs0, ri0)) = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, links(m, abs-dirs(fs0, ri0)) = ∅, m = 0, m = ROOT_INO, mkdir(m10, md0, 0, m12, ∅) = mkdir (m10 + 1, md0, 0, m12 + 1, abs-children (m, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3])), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 217:
fs0[ri0[dentrykey(m, str)]] = dentrynode(key, m), fs0[ri0[inodekey(m)]] = inodenode(key2, md6, true, 1, m12 + 1, m10 + 1), abs-children(m, fs0, ri0) = ∅, links(m, fs0, ri0) = ∅ ++ dentrykey(m, str), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0)[m, mkdir(m10, md0, 0, m12, ∅)], abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj((ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3], orphans(fs0, ri0) ++ inodekey(m), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m) ∈ ri0, asynced0 → boolvar0, ∀ key0. ¬ key0 ∈ ri0 ∨ ¬ key0.dentry? ∨ key0.ino ≠ m ⊦ # links(m, abs-dirs(fs0, ri0)) = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, links(m, abs-dirs(fs0, ri0)) = ∅, m = ROOT_INO, m = 0, mkdir(m10, md0, 0, m12, ∅) = mkdir (m10 + 1, md0, 0, m12 + 1, abs-children (m, fs0[adr1, inodenode(inodekey(m), md, true, 1, m12, m10)][adr2, dentrynode(dentrykey(m, str), 0)] [adr3, inodenode(inodekey(m), md0, true, 0, m12 + 1, m10 + 1) ], (ri0[inodekey(m), adr1] -- dentrykey(m, str))[inodekey(m), adr3])), adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ∅; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ dentrykeys(key0, ri) ↔ key ∈ ri ∧ key.dentry? ∧ key0.inode? ∧ key.ino = key0.ino; (s)