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Proof step 30 from proof abs-unshared-h (previous step)

(( (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 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
ad.meta = tree0[p0].meta, ad.size = # ad.entries, ((((((n1 => ad * abs(tree0[p0].entries, ad.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 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)% ⊦ ⌜bv⌝ (dirs) ↔ bv; (s)% ⊦ ((D ∧ D0))(dirs) ↔ D(dirs) ∧ D0(dirs); (s)%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-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]%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]% ⊦ (⌜bv⌝ ∧ D) * D0 = (⌜bv⌝ ∧ D * D0); (s)% ⊦ ((_∃ adD * D))(dirs) ↔ (∃ ad. ((adD(ad) * D))(dirs)); (s)