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Proof step 12 from proof afs-cons-inode-sync (previous step)

(ino = m ⊃ (files[m].size:= m2).meta:= md;mkfile(m0, md0, m1, content)) = mkfile(m3, md1, m4, content0), files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
(ino = m ⊃ (files[m].size:= m2).meta:= md;mkfile(m0, md0, m1, content)) = mkfile(m3, md1, m4, content0), files[ino] = mkfile(m0, md0, m1, content), dirs[ino] = mkdir(m5, md2, m6, m7, entries), afs-cons(dirs, files), m ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs → m6 = # links(ino, dirs) ∧ m6 ≤ 1 ∧ m5 = # entries ∧ m7 = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

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[ino], m5, md2, m6, m7, 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[ino], m5, md2, m6, m7, entries