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Proof step 81 from proof refine-mkdir (previous step)

fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), adr = adr3, fs = fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], key = inodekey(n), log = ((log0 + adr1 ') + adr2 ') + adr3 ', old_dent = negdentry(str), ri = ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2], ro = orphans(fs1, ri1), inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).inode?, inodenode(inodekey(n), md, true, 1, 0, 0).inode?, fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons(fs1, ri1), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]), log-cons(log0, fs1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), orphans-cons(fs1, ri1, orphans(fs1, ri1)), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1)), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri[key, adr]), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, asynced → boolvar0, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).trunc? ∨ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).inode?, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, inodenode(inodekey(n), md, true, 1, 0, 0).trunc? ∨ inodenode(inodekey(n), md, true, 1, 0, 0).inode? ⊦ ⟨p_inode0 := mkinode (m0, md2, true, inodenode(key0, md1, true, m1, m2, m6).nlink, inodenode(key0, md1, true, m1, m2, m6).nsubdirs, inodenode(key0, md1, true, m1, m2, m6).size); files := abs-files(fs1, ri1); dirs := abs-dirs(fs1, ri1); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]) ∧ files = abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]) ∧ orphans (abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]), abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr])) = abs-keys(orphans(fs1, ri1)) ∧ (asynced → boolvar) ∧ mkinode (m0, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).meta, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).directory, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nlink, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nsubdirs, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).size) = p_inode0 ∧ mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size) = p_inode1 ∧ mkdentry(str, n) = old_dent ∧ ESUCCESS = err0), adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, m1 = 0 ∧ m0 ≠ ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 82:
fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), adr = adr3, fs = fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], key = inodekey(n), log = ((log0 + adr1 ') + adr2 ') + adr3 ', old_dent = negdentry(str), p_inode0 = mkinode (m0, md2, true, inodenode(key0, md1, true, m1, m2, m6).nlink, inodenode(key0, md1, true, m1, m2, m6).nsubdirs, inodenode(key0, md1, true, m1, m2, m6).size), ri = ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2], ro = orphans(fs1, ri1), inodenode(inodekey(n), md, true, 1, 0, 0).inode?, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).inode?, inodenode(key0, md1, true, m1, m2, m6).inode?, orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), file-node-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]), file-node-cons(fs1, ri1), log-cons (log0, fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ]), log-cons(log0, fs1), orphans-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1)), orphans-cons(fs1, ri1, orphans(fs1, ri1)), replay-cons-strong (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri[key, adr]), ri-inj(ri1), ri-inj(fi), ubifs-cons (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), inodekey(m0) ∈ ri1, ri1[inodekey(m0)] ∈ fs1, asynced → boolvar0, inodenode(inodekey(n), md, true, 1, 0, 0).trunc? ∨ inodenode(inodekey(n), md, true, 1, 0, 0).inode?, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).trunc? ∨ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).inode?, inodenode(key0, md1, true, m1, m2, m6).trunc? ∨ inodenode(key0, md1, true, m1, m2, m6).inode? ⊦ ⟨files := abs-files(fs1, ri1); dirs := abs-dirs(fs1, ri1); afs_mkdir#(md; p_inode0, p_inode1, old_dent, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]) ∧ files = abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]) ∧ orphans (abs-dirs (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr]), abs-files (fs1[adr1, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1)][adr2, dentrynode(dentrykey(m0, str), n)] [adr3, inodenode(inodekey(n), md, true, 1, 0, 0) ], ri[key, adr])) = abs-keys(orphans(fs1, ri1)) ∧ (asynced → boolvar) ∧ mkinode (m0, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).meta, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).directory, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nlink, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).nsubdirs, inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1).size) = p_inode0 ∧ mkinode (n, inodenode(inodekey(n), md, true, 1, 0, 0).meta, inodenode(inodekey(n), md, true, 1, 0, 0).directory, inodenode(inodekey(n), md, true, 1, 0, 0).nlink, inodenode(inodekey(n), md, true, 1, 0, 0).nsubdirs, inodenode(inodekey(n), md, true, 1, 0, 0).size) = p_inode1 ∧ mkdentry(str, n) = old_dent ∧ ESUCCESS = err0), adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, n = 0, adr3 ∈ fs1, adr2 ∈ fs1, adr1 ∈ fs1, inodekey(n) ∈ ri1, inodekey(n) ∈ fo, dentrykey(m0, str) ∈ ri1, m1 = 0 ∧ m0 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)