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Proof step 163 from proof refine-mkdir (previous step)

dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), files0 = files, ino = inode.ino, inode = mkinode(ino1, md1, true, # links(ino1, dirs0), m1, # entries0), ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs1), mkdentry(str, ino2).dentry?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino ∈ dirs1, ino1 ∈ dirs0, ino2 ∈ dirs4, dirs ≡ dirs1[ino, dirs1[ino].meta:= inode.meta], dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], dirs4 ≡ dirs3 ++ ino2, dirs1 ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err2), ino ∈ files, str ∈ entries0, ino2 ∈ files, ino2 ∈ dirs0, ino2 ∈ dirs3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 164:
dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs1), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino2 ∈ dirs4, ino1 ∈ dirs0, ino1 ∈ dirs1, dirs1 ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], dirs4 ≡ dirs3 ++ ino2, dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], dirs ≡ dirs1[ino1, dirs1[ino1].meta:= md1], ¬ ino2 ∈ dirs0, ¬ ino2 ∈ files, ¬ str ∈ entries0, ¬ ino2 ∈ dirs3, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files), abs-of(of); err2, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err2)

Rule argument

Additional information

Used simplifier rules: assign-new-other: ⊦ dirs ≡ dirs0[ino, ad] ∧ ¬ ino0 ∈ dirs0 ∧ ino ∈ dirs0 → ¬ ino0 ∈ dirs; (forward) from specification separation[dir-heap]% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)