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Proof step 5 from proof afs-cons-remove-orphans (previous step)

afs-cons(dirs, files) ⊦ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, 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 ∈ orphans(dirs, files) → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ ( ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∧ ¬ dirs[ino].entries[name] ∈ orphans(dirs, files) ∨ dirs[ino].entries[name] ∈ files ∧ ¬ dirs[ino].entries[name] ∈ orphans(dirs, files)) ∧ (ino ∈ files ∧ ¬ ino ∈ orphans(dirs, files) ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
files[ino] = mkfile(m, md, m0, content), afs-cons(dirs, files) ⊦ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, 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 ∈ orphans(dirs, files) → ¬ ino ∈ dirs ∧ m0 = # links(ino, dirs)) ∧ ( ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∧ ¬ dirs[ino].entries[name] ∈ orphans(dirs, files) ∨ dirs[ino].entries[name] ∈ files ∧ ¬ dirs[ino].entries[name] ∈ orphans(dirs, files)) ∧ (ino ∈ files ∧ ¬ ino ∈ orphans(dirs, files) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[ino], m, md, m0, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[ino], m, md, m0, content