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Proof step 37 from proof inv-open (previous step)

dom of < ino1, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, p, ROOT_INO, dirs, files), n ∈ of[ino1, mkfile(ino0, mode, 0)], n ∈ of, of[n].ino ∈ files, ino0 ∈ files ⊦ of[ino1, mkfile(ino0, mode, 0)][n].ino ∈ files, ino0 ∈ dirs, (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, files[ino0].meta), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, files[ino0].meta)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
files[ino0] = mkfile(m, md, m0, content), dom of < ino1, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files, of[n].ino ∈ files, n ∈ of, n ∈ of[ino1, mkfile(ino0, mode, 0)] ⊦ ino0 ∈ dirs, of[ino1, mkfile(ino0, mode, 0)][n].ino ∈ files, (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md)

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, 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[ino0], m, md, m0, content