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Proof step 2 from proof refine-readdir (previous step)

dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), orphans(dirs, files) = abs-keys(ro), strings = strings0, fo.inodes?, ro.inodes?, afs-cons(dirs, files), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-readdir(inode.ino, dirs, files), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), asynced → boolvar ⊦ ⟪aubifs_readdir#(inode, ri, fi, ro, fo, fs, log, boolvar; strings, err)⟫ ⟨afs_readdir#(inode, dirs, files, asynced; strings0, err0)⟩ ( (dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(dirs, files) = abs-keys(ro) ∧ (asynced → boolvar)) ∧ strings = strings0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
err = err0, strings = strings0, fs[ri[inodekey(inode.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(inode.ino) ∈ ri, asynced → boolvar ⊦ ⟪aubifs_readdir#(inode, ri, fi, orphans(fs, ri), fo, fs, log, boolvar; strings, err)⟫ ⟨afs_readdir#(inode, abs-dirs(fs, ri), abs-files(fs, ri), asynced; strings0, err0)⟩ ((asynced → boolvar) ∧ strings = strings0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ pre-readdir(ino, dirs, files) ↔ valid-dir-ino(ino, dirs, files); (s)%⊦ ro.inodes? → (abs-keys(ro) = abs-keys(orphans(fs, ri)) ↔ ro = orphans(fs, ri)); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)