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Proof step 30 from proof write-inode-inv (previous step)

files1 -- ino = files0 -- ino, files0[ino] = mkfile(m, md, m0, content0), files1[ino] = mkfile(m, md, # links(ino, dirs), content), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ino ∈ files0, ino ∈ files1, n ≤ # buf, n1 ≤ # buf, n ≤ n1 ⊦ ∀ ino0, name, n0. ROOT_INO ∈ dirs ∧ (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dir-empty(ino0, dirs, files1)) ∧ ( ino0 ∈ dirs → ¬ ino0 ∈ files1 ∧ dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs)) ∧ (ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ files1[ino0].nlink = # links(ino0, dirs)) ∧ (ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → valid-ino(dirs[ino0].entries[name], dirs, files1)) ∧ (ino0 ∈ files1 ∧ n0 ∈ files1[ino0].content → valid-pagesize(ino0, n0, files1)) → ROOT_INO ∈ dirs ∧ ( ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dir-empty(ino0, dirs, files1[ino, mkfile(m + n, md, # links(ino, dirs), content)])) ∧ ( ino0 ∈ dirs → ¬ ino0 ∈ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)] ∧ dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs)) ∧ ( ino0 ∈ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)] → ¬ ino0 ∈ dirs ∧ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)][ino0].nlink = # links(ino0, dirs)) ∧ ( ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → valid-ino(dirs[ino0].entries[name], dirs, files1[ino, mkfile(m + n, md, # links(ino, dirs), content)])) ∧ ( ino0 ∈ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)] ∧ n0 ∈ files1[ino, mkfile(m + n, md, # links(ino, dirs), content)][ino0].content → valid-pagesize(ino0, n0, files1[ino, mkfile(m + n, md, # links(ino, dirs), content)]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
files1 -- ino = files0 -- ino, files1[ino] = mkfile(m, md, # links(ino, dirs), content), files0[ino] = mkfile(m, md, m0, content0), afs-cons(dirs, files1), write-inv(0, n1, buf, n, content0, content), ROOT_INO ∈ dirs, ino ∈ files1, ino ∈ files0, n ≤ n1, n1 ≤ # buf, n ≤ # buf, ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ files1[ino0].nlink = # links(ino0, dirs), ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅, ino0 ∈ dirs → dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files1, ino0 ∈ files1 ∧ n0 ∈ files1[ino0].content → # files1[ino0].content[n0] = VFS_PAGE_SIZE ⊦ (ino0 ∈ files1 → ¬ ino0 ∈ dirs ∧ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).nlink = # links(ino0, dirs)) ∧ ( ino0 ∈ files1 ∧ n0 ∈ (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content → # (ino0 = ino ⊃ mkfile(m + n, md, # links(ino, dirs), content);files1[ino0]).content[n0] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)%⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)