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Proof step 32 from proof afs-cons-reduce (previous step)

dirs0[ino] = mkdir(m6, md2, m7, m8, entries0), files0[ino] = mkfile(m4, md1, m5, content0), files1[ino] = mkfile(m, md, m0, content), dirs1[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs0, files0) ⊦ ROOT_INO ∈ dirs1 ∧ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → entries = ∅) ∧ (ino ∈ dirs1 → ¬ ino ∈ files1 ∧ m2 = # links(ino, dirs1) ∧ # links(ino, dirs1) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs1)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs1 ∧ m0 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ entries → entries[name] ∈ dirs1 ∨ entries[name] ∈ files1) ∧ (ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE), (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m6 = # entries0 ∧ m8 = # subdirs(ino, dirs0)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ afs-cons(dirs, files) ↔ (∀ ino. ROOT_INO ∈ dirs ∧ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files)) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files)))
Proof step 34:
dirs1[ino] = mkdir(m1, md0, m2, m3, entries), files1[ino] = mkfile(m, md, m0, content), files0[ino] = mkfile(m4, md1, m5, content0), dirs0[ino] = mkdir(m6, md2, m7, m8, entries0), ∀ ino. ROOT_INO ∈ dirs0 ∧ (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files0)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files0 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0)) ∧ (∀ name. ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino(dirs0[ino].entries[name], dirs0, files0)) ∧ (∀ n. ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) ⊦ (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m6 = # entries0 ∧ m8 = # subdirs(ino, dirs0)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files0), ROOT_INO ∈ dirs1 ∧ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → entries = ∅) ∧ (ino ∈ dirs1 → ¬ ino ∈ files1 ∧ m2 = # links(ino, dirs1) ∧ # links(ino, dirs1) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs1)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs1 ∧ m0 = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ entries → entries[name] ∈ dirs1 ∨ entries[name] ∈ files1) ∧ (ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE)

Rule argument

spec: afs-base name: afs-cons seq: ⊦ afs-cons(dirs, files) ↔ (∀ ino. ROOT_INO ∈ dirs ∧ ( ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files)) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files)) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → valid-pagesize(ino, n, files))) subst: [files, dirs] → [files0, dirs0] flags: <all paths>

Additional information

Used terms: files0, dirs0