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Proof step 57 from proof refine-lookup (previous step)

dent = old_dent, fs[ri[inodekey(p_ino)]].directory, fo.inodes?, orphans(fs, ri).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(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_ino) ∈ ri, ⌊err0⌋ , asynced → boolvar1, links(p_ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_ino = ROOT_INO, fs[ri[inodekey(p_ino)]].nlink ≠ 0 ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ ((asynced → boolvar1) ∧ err0 = err), ⟨if old_dent.name ∈ abs-dir(p_ino, fs, ri).entries then {dent := mkdentry(dent.name, abs-dir(p_ino, fs, ri).entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ ((asynced → boolvar1) ∧ old_dent = dent ∧ err0 = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
abs-dir(p_ino, fs, ri) = mkdir(m, md, m0, m1, 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), inodekey(p_ino) ∈ ri, ⌊err0⌋ , 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) ∧ err0 = 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) ∧ old_dent = dent ∧ err0 = err)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [abs-dir(p_ino, fs, ri), m, md, m0, m1, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: abs-dir(p_ino, fs, ri), m, md, m0, m1, entries