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Proof step 109 from proof inv-rmdir (previous step)

dirs[entries[str]].size = 0, dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m1, entries), err = ESUCCESS, entries[str] ≠ ROOT_INO, dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, entries[str] ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md, true, # links(ino1, dirs), m1, m) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); dent := mkdentry(str, dirs[ino1].entries[str]); p_inode := getinode(mkdentry(str, entries[str]).ino, dirs, files); afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 110:
dirs[ino1] = mkdir(m, md, # links(ino1, dirs), m1, entries), dirs[entries[str]] = mkdir(m0, md0, m2, m3, entries0), err = ESUCCESS, m0 = 0, dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), entries[str] ∈ dirs, str ∈ entries, ino1 ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md, true, # links(ino1, dirs), m1, m) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); dent := mkdentry(str, dirs[ino1].entries[str]); p_inode := getinode(mkdentry(str, entries[str]).ino, dirs, files); afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), entries[str] = ROOT_INO

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[entries[str]], m0, md0, m2, m3, entries0]

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[entries[str]], m0, md0, m2, m3, entries0