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Proof step 122 from proof refine-write-inode (previous step)

fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), adr1 ≠ ri[inodekey(ino)], ino ≠ m, m ≠ 0, fs0[ri[inodekey(ino)]].directory, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)[m, mkfile(m2, md, m0, abs-content(m, fs0, ri))]), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(ino) ∈ ri, inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, ¬ adr1 ∈ fs0, asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), (dentrykey(ino, str) ∈ ri → dentrykey(ino, str) ∈ ri[inodekey(m), adr1]) ∧ ( dentrykey(ino, str) ∈ ri → fs0[ri[dentrykey(ino, str)]].ino = (adr1 = ri[dentrykey(ino, str)] ⊃ inodenode(inodekey(m), md, false, m0, 0, m2);fs0[ri[dentrykey(ino, str)]]).ino)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 123:
fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), fs0[ri[inodekey(ino)]].directory, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)[m, mkfile(m2, md, m0, abs-content(m, fs0, ri))]), afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, asynced0 → boolvar1 ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ abs-files(fs0, ri) = abs-files(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) ∧ orphans(fs0[adr1, inodenode(inodekey(m), md, false, m0, 0, m2)], ri[inodekey(m), adr1]) = orphans(fs0, ri) ∧ (asynced0 → boolvar) ∧ ESUCCESS = err), adr1 = ri[inodekey(ino)], ino = m, m = 0, adr1 ∈ fs0, (dentrykey(ino, str) ∈ ri → dentrykey(ino, str) ∈ ri[inodekey(m), adr1]) ∧ ( dentrykey(ino, str) ∈ ri → fs0[ri[dentrykey(ino, str)]].ino = (adr1 = ri[dentrykey(ino, str)] ⊃ inodenode(inodekey(m), md, false, m0, 0, m2);fs0[ri[dentrykey(ino, str)]]).ino)

Rule argument

fma: dentrykey(ino, str) ∈ ri

Additional information

Used formulas: dentrykey(ino, str) ∈ ri