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Proof step 43 from proof abs-has-rootpath-h (previous step)

dirs2[ino0] = mkdir(m, md0, m1, m2, entries1), ((ino0 => mkdir(n0, md, m0, n, entries0) * {dirs0} * abs(sdt0, sdi)))(dirs2), ((abs(tree, ino1) * abs(sdt0, sdi) * {dirs0} * ino0 => mkdir(n0, md, m0, n, entries0)))(dirs1 ∪ dirs2), abs(tree, ino1)(dirs1), ispath(p, ino1, ino, dirs1, files), ino ∈ dirs1, sdi[str, ino1] ⊆ entries0, dirs1 ⊥ dirs2, ∀ sdt1, ino0, n0, md, m0, n, entries0, entries, dirs0, dirs, ino, files. # sdt1 < # sdt0[str, tree] → (((ino0 => mkdir(n0, md, m0, n, entries0) * abs(sdt1, entries)) * {dirs0} ))(dirs) ∧ ino ∈ dirs ∧ entries ⊆ entries0 ∧ (∀ str. str ∈ sdt1 → (∀ ino, dirs, ino0, dirs0, files. ino ∈ dirs ∧ ((abs(sdt1[str], ino0) * {dirs0} ))(dirs) → ino ∈ dirs0 ∨ (∃ p. ispath(p, ino0, ino, dirs, files)))) → ino ∈ dirs0 ∨ (∃ p. ispath(p, ino0, ino, dirs, files)) ⊦ ino ∈ dirs0, str ∈ sdi, str ∈ sdt0, ino0 ∈ dirs1, str ∈ entries1 ∧ ispath(p, entries1[str], ino, dirs1 ∪ dirs2, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
((ino0 => mkdir(n0, md, m0, n, entries1) * {dirs0} * abs(sdt0, sdi)))(dirs2), ((abs(tree, ino1) * abs(sdt0, sdi) * {dirs0} * ino0 => mkdir(n0, md, m0, n, entries1)))(dirs1 ∪ dirs2), abs(tree, ino1)(dirs1), ispath(p, ino1, ino, dirs1, files), ino ∈ dirs1, sdi[str, ino1] ⊆ entries1, dirs1 ⊥ dirs2, ∀ sdt1, ino0, n0, md, m0, n, entries0, entries, dirs0, dirs, ino, files. # sdt1 < # sdt0[str, tree] → (((ino0 => mkdir(n0, md, m0, n, entries0) * abs(sdt1, entries)) * {dirs0} ))(dirs) ∧ ino ∈ dirs ∧ entries ⊆ entries0 ∧ (∀ str. str ∈ sdt1 → (∀ ino, dirs, ino0, dirs0, files. ino ∈ dirs ∧ ((abs(sdt1[str], ino0) * {dirs0} ))(dirs) → ino ∈ dirs0 ∨ (∃ p. ispath(p, ino0, ino, dirs, files)))) → ino ∈ dirs0 ∨ (∃ p. ispath(p, ino0, ino, dirs, files)) ⊦ ino ∈ dirs0, str ∈ sdi, str ∈ sdt0, ino0 ∈ dirs1, str ∈ entries1 ∧ ispath(p, entries1[str], ino, dirs1 ∪ dirs2, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ((ino => ad * D))(dirs) → (dirs[ino] = ad0 ↔ ad = ad0); (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]