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Proof step 6 from proof abs-acyclic (previous step)

entries[str] = ROOT_INO, dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), ino ∈ dirs, str ∈ entries ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 7:
⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1))
Proof step 8:
dirs[ino] = mkdir(# entries, md, # links(ino, dirs), m0, entries), entries[str] = ROOT_INO, tree[p].dir?, abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ entries, ino ∈ dirs, p ∈ tree → abs(tree, ROOT_INO) = _∃(λ ino1. abs|(tree, ROOT_INO, p, ino1) * abs(tree[p], ino1)) ⊦

Rule argument

spec: vfs-abs name: path-unfold seq: ⊦ p ∈ tree → abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)) subst: [p, tree, ino0] → [p, tree, ROOT_INO]

Additional information

Used terms: p, tree, ROOT_INO