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Proof step 12 from proof orphans-del-file (previous step)

# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), afs-cons(dirs, files), ino ∈ files, ino0 ∈ dirs → dirs[ino0].nlink = 0, ino0 ∈ files → files[ino0].nlink = 0, ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files ⊦ ino0 = ROOT_INO, ino ∈ dirs, ino0 ≠ ino ∧ (ino0 ∈ dirs ∨ ino0 ∈ files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), files[ino0] = mkfile(m, md0, m0, content0), afs-cons(dirs, files), ino ∈ files, ino0 ∈ files → m0 = 0, ino0 ∈ dirs → dirs[ino0].nlink = 0, ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files ⊦ ino0 = ROOT_INO, ino ∈ dirs, ino0 ≠ ino ∧ (ino0 ∈ dirs ∨ ino0 ∈ files)

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[ino0], m, md0, 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[ino0], m, md0, m0, content