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Proof step 31 from proof refine-lookup (previous step)

fs[ri[dentrykey(p_ino, old_dent.name)]] = dentrynode(key, m), abs-dir(p_ino, fs, ri) = mkdir(m0, md, m1, m2, entries), dent = old_dent, fs[ri[inodekey(p_ino)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(p_ino, old_dent.name) ∈ ri, ri[dentrykey(p_ino, old_dent.name)] ∈ fs, inodekey(p_ino) ∈ ri, asynced → boolvar1, fs[ri[inodekey(p_ino)]].nlink ≠ 0 ∨ p_ino = ROOT_INO, links(p_ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ ((asynced → boolvar1) ∧ mkdentry(old_dent.name, m) = old_dent ∧ ESUCCESS = err), ⟨if old_dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ ((asynced → boolvar1) ∧ mkdentry(old_dent.name, m) = dent ∧ ESUCCESS = err)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
fs[ri[dentrykey(p_ino, old_dent.name)]] = dentrynode(key, m), fs[ri[inodekey(p_ino)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(p_ino, old_dent.name) ∈ ri, ri[dentrykey(p_ino, old_dent.name)] ∈ fs, inodekey(p_ino) ∈ ri, asynced → boolvar1, fs[ri[inodekey(p_ino)]].nlink ≠ 0 ∨ p_ino = ROOT_INO, links(p_ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨dent := mkdentry(old_dent.name, abs-children(p_ino, fs, ri)[old_dent.name]); err := ESUCCESS⟩ ((asynced → boolvar1) ∧ mkdentry(old_dent.name, m) = dent ∧ ESUCCESS = err), ⟨fail#(; ; err)⟩ ((asynced → boolvar1) ∧ mkdentry(old_dent.name, m) = old_dent ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)