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Proof step 6 from proof inv-recovery (previous step)

afs-cons(dirs0, files1), ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅, ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ files1 → ¬ ino ∈ dirs0 ∧ files1[ino].nlink = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files1, ino ∈ files1 ∧ n ∈ files1[ino].content → # files1[ino].content[n] = VFS_PAGE_SIZE ⊦ (ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) → ¬ ino ∈ dirs0 ∧ files1[ino].nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∧ ¬ dirs0[ino].entries[name] ∈ orphans(dirs0, files1) ∨ dirs0[ino].entries[name] ∈ files1 ∧ ¬ dirs0[ino].entries[name] ∈ orphans(dirs0, files1)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ n ∈ files1[ino].content → # files1[ino].content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
files1[ino] = mkfile(m, md, m0, content), afs-cons(dirs0, files1), ROOT_INO ∈ dirs0, ino ∈ files1 ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE, ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∨ dirs0[ino].entries[name] ∈ files1, ino ∈ files1 → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0), ino ∈ dirs0 → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅ ⊦ (ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dirs0[ino].entries = ∅) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) → dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ name ∈ dirs0[ino].entries → dirs0[ino].entries[name] ∈ dirs0 ∧ ¬ dirs0[ino].entries[name] ∈ orphans(dirs0, files1) ∨ dirs0[ino].entries[name] ∈ files1 ∧ ¬ dirs0[ino].entries[name] ∈ orphans(dirs0, files1)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ 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] → [files1[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: files1[ino], m, md, m0, content