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Proof step 33 from proof abs-unshared-h (previous step)

(( ( ( ((n1 => mkdir(# entries, tree0[p0].meta, m0, m1, entries) * abs(tree0[p0].entries, entries)) * abs|(tree1, ino1, p1, n1)) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1)) * D) )(dirs), tree0[p0].dir?, ispath(p0, ino0, n1, dirs, files), ispath(p1, ino1, n1, dirs, files), p0 ∈ tree0, 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 34:
⊦ tree.dir? → abs(tree, ino) = _∃(λ ad. ino => ad * abs(tree.entries, ad.entries) ∧ ⌜ad.meta = tree.meta⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 35:
(( ( ( ((n1 => mkdir(# entries, tree0[p0].meta, m0, m1, entries) * abs(tree0[p0].entries, entries)) * abs|(tree1, ino1, p1, n1)) * abs(tree1[p1], n1)) * abs|(tree0, ino0, p0, n1)) * D) )(dirs), tree0[p0].dir?, ispath(p1, ino1, n1, dirs, files), ispath(p0, ino0, n1, dirs, files), p1 ∈ tree1, p0 ∈ tree0, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ tree1[p1].dir?

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, tree1[p1]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ((_∃ adD * D))(dirs) ↔ (∃ ad. ((adD(ad) * D))(dirs)); (s)% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)% ⊦ ino => ad * ino => ad0 = false; (s)% ⊦ false * D = false; (s)%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]% ⊦ (false ∧ D) = false; (s)%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]%and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]% ⊦ ¬ false(dirs); (s) Used terms: n1, tree1[p1]