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Proof step 173 from proof refine-mkdir (previous step)

fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), (abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[m0] = mkdir(m, md0, m3, m4, entries), orphans(fs1, ri1).inodes?, fo.inodes?, afs-cons(abs-dirs(fs1, ri1), abs-files(fs1, ri1)), afs-cons ((abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m3, m4, entries) ], 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs1, ri1, orphans(fs1, ri1), fi, fo, log0), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], 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, asynced0 → boolvar0, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO, m1 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = n, 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, ( inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ∧ ¬ (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory ↔ inodekey(ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ∧ ¬ (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory → 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]) [ino ] = mkfile(fs1[ri1[inodekey(ino)]].size, fs1[ri1[inodekey(ino)]].meta, fs1[ri1[inodekey(ino)]].nlink, abs-content(ino, fs1, ri1)))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 174:
(abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[m0] = mkdir(m, md0, m3, m4, entries), fs1[ri1[inodekey(m0)]] = inodenode(key0, md1, true, m1, m2, m6), fo.inodes?, orphans(fs1, ri1).inodes?, afs-cons ((abs-dirs(fs1, ri1)[m0, mkdir(m6 + 1, md1, m1, m2 + 1, abs-children(m0, fs1, ri1)[str, n])] ++ n)[n, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m3, m4, entries) ], abs-files(fs1, ri1)), 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri1), ri-inj(ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]), 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], orphans(fs1, ri1), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri1[inodekey(m0)] ∈ fs1, inodekey(m0) ∈ ri1, inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3], asynced0 → boolvar0, m1 ≠ 0 ∨ m0 = ROOT_INO, links(m0, abs-dirs(fs1, ri1)) ≠ ∅ ∨ m0 = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, ino = n, m0 = 0, n = 0, dentrykey(m0, str) ∈ ri1, inodekey(n) ∈ fo, inodekey(n) ∈ ri1, adr1 ∈ fs1, adr2 ∈ fs1, adr3 ∈ fs1, ( inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ∧ ¬ (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory ↔ inodekey(ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3] ∧ ¬ (adr3 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(n), md, true, 1, 0, 0) ;(adr2 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ dentrynode(dentrykey(m0, str), n) ;(adr1 = (m0 = ino ⊃ adr1;ri1[inodekey(ino)]) ⊃ inodenode(inodekey(m0), md2, true, m1, m2 + 1, m6 + 1) ;fs1[(m0 = ino ⊃ adr1;ri1[inodekey(ino)])] ) ) ) .directory → 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) ], ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]) [ino ] = mkfile(fs1[ri1[inodekey(ino)]].size, fs1[ri1[inodekey(ino)]].meta, fs1[ri1[inodekey(ino)]].nlink, abs-content(ino, fs1, ri1))), m1 = 0 ∧ m0 ≠ ROOT_INO

Rule argument

fma: inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2] [inodekey(n), adr3 ]

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las) Used formulas: inodekey(ino) ∈ ri1[inodekey(m0), adr1][dentrykey(m0, str), adr2][inodekey(n), adr3]