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Proof step 17 from proof abs-fold-new-p (previous step)

tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * abs(sdt, entries) * D))(dirs), p ∈ tree, D ⊆ abs(tree0, ino1) ⊦ (( ( ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * (⌜str ∈ entries[str, ino1]⌝ ∧ abs(tree0, entries[str, ino1][str]) * abs(sdt, entries[str, ino1] -- str))) * abs|(tree[p, dnode(md, sdt[str, tree0])], ROOT_INO, p, ino0)) )(dirs), str ∈ entries, str ∈ sdt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * abs(sdt, entries) * D))(dirs), p ∈ tree, D ⊆ abs(tree0, ino1) ⊦ (( ino0 => mkdir(# entries + 1, md, m0, m1, entries[str, ino1]) * (abs(tree0, ino1) * abs(sdt, entries)) * abs|(tree[p, dnode(md, sdt[str, tree0])], ROOT_INO, p, ino0)) )(dirs), str ∈ sdt, str ∈ entries

Rule argument

Additional information

Used simplifier rules: 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]% ⊦ (true ∧ D) = D; (s)% ⊦ ((abs(sdt, sdi) * D))(dirs) ∧ ¬ str ∈ sdt → sdi -- str = sdi; (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]% ⊦ entries[str, ino] -- str = entries -- str; (s)% ⊦ entries[str, ino][str] = ino; (s)% ⊦ ⌜true⌝ = true; (s)% ⊦ str ∈ entries[str, ino]; (s)