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Proof step 183 from proof inv-rmdir (previous step)

dirs0[entries[str]] = mkdir(0, md, # links(entries[str], dirs0), m4, ∅), dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), dirs = dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2 - 1, entries -- str)] [entries[str], mkdir(0, md, # links(entries[str], dirs0) - 1, m4, ∅) ], err = ESUCCESS, # links(entries[str], dirs0) ≠ 0, entries[str] ≠ ROOT_INO, entries[str] ≠ ino1, m ≠ 0, m2 ≠ 0, dom of < ino0, afs-cons(dirs0, files), afs-cons (dirs0[ino1, mkdir(m - 1, md1, # links(ino1, dirs0), m2 - 1, entries -- str)] [entries[str], mkdir(0, md, # links(entries[str], dirs0) - 1, m4, ∅) ], 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), ino1 ∈ dirs0, str ∈ entries, entries[str] ∈ dirs0, 1 ≤ m, 1 ≤ m2, 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 184:
dirs0[ino1] = mkdir(m, md1, # links(ino1, dirs0), m2, entries), dirs0[entries[str]] = mkdir(0, md, # links(entries[str], dirs0), m4, ∅), dirs = dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m2 - 1, entries -- str)] [entries[str], mkdir(0, md, # links(entries[str], dirs0) - 1, m4, ∅) ], err = ESUCCESS, m = m0 + 1, dom of < ino0, afs-cons (dirs0[ino1, mkdir(m0, md1, # links(ino1, dirs0), m2 - 1, entries -- str)] [entries[str], mkdir(0, md, # links(entries[str], dirs0) - 1, 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), 1 ≤ m2, 1 ≤ m, 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, m = 0, m2 = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m0