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Proof step 34 from proof inv-seek (previous step)

of[fd] = mkfile(m, mode, m0), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n0 ∈ of[fd, mkfile(m, mode, files[m].size + n)], n0 ∈ of, of[n0].ino ∈ files ⊦ of[fd, mkfile(m, mode, files[m].size + n)][n0].ino ∈ files

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), of[n0].ino ∈ files, n0 ∈ of, n0 ∈ of[fd, mkfile(m, mode, m1 + n)], fd ∈ of ⊦ of[fd, mkfile(m, mode, m1 + n)][n0].ino ∈ 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[m], m1, md, m2, 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[m], m1, md, m2, content