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Proof step 82 from proof refine-mkdir (previous step)

dent = negdentry(str), err = ESUCCESS, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, dirs[ino1].meta), px(user, dirs[ino1].meta), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ [afs_lookup#(ino1, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); afs_mkdir#(md; inode, c_inode, dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 83:
dirs[ino1] = mkdir(m, md0, m0, m1, entries), dent = negdentry(str), err = ESUCCESS, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ [afs_lookup#(ino1, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {dent := negdentry((q + str ').last); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, m0, m1, m);mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size)); afs_mkdir#(md; inode, c_inode, dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

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] → [dirs[ino1], m, md0, 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: dirs[ino1], m, md0, m0, m1, entries