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Proof step 188 from proof inv-rmdir (previous step)

# links(entries[str], dirs0) = m1 + 1, dirs0[ino1] = mkdir(m0 + 1, md1, # links(ino1, dirs0), m + 1, entries), dirs0[entries[str]] = mkdir(0, md, # links(entries[str], dirs0), m4, ∅), dirs = dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], err = ESUCCESS, dom of < ino0, afs-cons(dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], files), afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), entries[str] ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, 1 ≤ # links(entries[str], dirs0), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪vfs_put_inode#(getinode(entries[str], dirs, files), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), # links(entries[str], dirs0) = 0, entries[str] = ROOT_INO, entries[str] = ino1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 189:
# links(entries[str], dirs0) = m1 + 1, dirs0[ino1] = mkdir(m0 + 1, md1, # links(ino1, dirs0), m + 1, entries), dirs0[entries[str]] = mkdir(0, md, m1 + 1, m4, ∅), dirs = dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], err = ESUCCESS, entries[str] ≠ ROOT_INO, entries[str] ≠ ino1, dom of < ino0, afs-cons(dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m, entries -- str)][entries[str], mkdir(0, md, m1, m4, ∅)], files), afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), entries[str] ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪vfs_put_inode#(getinode(entries[str], dirs, files), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base