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Proof step 12 from proof py (previous step)

tree[p].dir? ↔ m ∈ dirs, abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ino, m, dirs, files), px(user, p, ino, dirs, files) ⊦ pw(user, p, tree, abs-files(files)) ↔ pw(user, p, ino, dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)))
Proof step 14:
tree[p].dir? ↔ m ∈ dirs, abs(tree, ino)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ino, m, dirs, files), px(user, p, ino, dirs, files), px-parent(user, p, ino, dirs, files) ⊦ pw(user, meta(ε, m, dirs, files)) ↔ pw(user, p, ino, dirs, files)

Rule argument

spec: <toplevel> name: pw seq: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files))) subst: [ino, m, dirs, ofh, files, tree, p, user] → [ino, m, dirs, ofh, files, tree, p, user] flags: <all paths>

Additional information

Used simplifier rules: ⊦ px(user, p, ino, dirs, files) → px-parent(user, p, ino, dirs, files); (s) Used terms: ino, m, dirs, ofh, files, tree, p, user