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Proof step 5 from proof afs-cons-pagesize (previous step)

files[ino] = mkfile(m, md, # links(ino, dirs), content), n ∈ content, ino ∈ 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)) ⊦ # content[n] = VFS_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
files[ino] = mkfile(m, md, # links(ino, dirs), content), ino ∈ files, n ∈ content, ROOT_INO ∈ dirs, ∀ ino0. (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → dirs[ino0].entries = ∅) ∧ ( ino0 ∈ dirs → ¬ ino0 ∈ files ∧ dirs[ino0].nlink = # links(ino0, dirs) ∧ dirs[ino0].nlink ≤ 1 ∧ dirs[ino0].size = # dirs[ino0].entries ∧ dirs[ino0].nsubdirs = # subdirs(ino0, dirs)) ∧ (ino0 ∈ files → ¬ ino0 ∈ dirs ∧ files[ino0].nlink = # links(ino0, dirs)) ∧ (∀ name. ino0 ∈ dirs ∧ name ∈ dirs[ino0].entries → dirs[ino0].entries[name] ∈ dirs ∨ dirs[ino0].entries[name] ∈ files) ∧ (∀ n0. ino0 ∈ files ∧ n0 ∈ files[ino0].content → # files[ino0].content[n0] = VFS_PAGE_SIZE) ⊦ # content[n] = VFS_PAGE_SIZE

Rule argument

Additional information

Used simplifier rules: dir-empty: ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅;%valid-ino: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files;%valid-pagesize: ⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE;