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Proof step 17 from proof abs-unshared-h (previous step)

(((abs|(tree1, ino1, p1, n1) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1) * abs(tree0[p0], n1) * D))(dirs), ispath(p0, ino0, n1, dirs, files), ispath(p1, ino1, n1, dirs, files), p0 ∈ tree0, n1 ∈ dirs, p1 ∈ tree1, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ tree.dir? → abs(tree, ino) = _∃(λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 19:
(((abs|(tree1, ino1, p1, n1) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1) * abs(tree0[p0], n1) * D))(dirs), ispath(p1, ino1, n1, dirs, files), ispath(p0, ino0, n1, dirs, files), p1 ∈ tree1, n1 ∈ dirs, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ tree0[p0].dir?
Proof step 30:
(( (abs|(tree1, ino1, p1, n1) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1) * _∃(λ ad. n1 => ad * abs(tree0[p0].entries, ad.entries) ∧ ⌜ad.meta = tree0[p0].meta⌝ ∧ ⌜ad.size = # ad.entries⌝ ) * D) )(dirs), tree0[p0].dir?, ispath(p1, ino1, n1, dirs, files), ispath(p0, ino0, n1, dirs, files), p1 ∈ tree1, n1 ∈ dirs, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦

Rule argument

spec: <toplevel> name: abs-is-dnode seq: ⊦ tree.dir? → abs(tree, ino) = _∃ (λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ ) subst: [ino, tree] → [n1, tree0[p0]] flags: <all paths>

Additional information

Used terms: n1, tree0[p0]