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Proof step 104 from proof refine-readmeta (previous step)

(ino2 ∈ dirs ⊃ mkinode(ino2, dirs[ino2].meta, true, dirs[ino2].nlink, dirs[ino2].nsubdirs, dirs[ino2].size) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ) = mkinode(m, md, boolvar, m0, m1, m2), root[path].dir? ↔ ino2 ∈ dirs, ¬ boolvar, root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced, ino2 ∈ dirs ∨ ino2 ∈ files ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ m0 = ino4 ∧ m2 = ino3 ∧ ESUCCESS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 106:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 107:
root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, files[m].meta), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, m ∈ files, ¬ root[path].dir?, ¬ m ∈ dirs, psynced → asynced ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ files[m].meta = md0 ∧ files[m].nlink = ino4 ∧ files[m].size = ino3 ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ tree[ε] = tree; (s)