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Proof step 205 from proof refine-readmeta (previous step)

p0.last = q.last, root[p0] = fnode(⌜m⌝ ), root[q] = fnode(⌜m⌝ ), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), lookup(parent(p0), ROOT_INO, dirs, files) = lookup(parent(q), ROOT_INO, dirs, files), root.dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, m8, dirs, files), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), p0 ∈ root, m ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, p0 = q, root[path].dir?, m8 ∈ dirs, m ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 206:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 207:
⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files))
Proof step 208:
⊦ 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 209:
p0.last = q.last, dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), root[q] = fnode(⌜m⌝ ), root[p0] = fnode(⌜m⌝ ), lookup(parent(p0), ROOT_INO, dirs, files) = lookup(parent(q), ROOT_INO, dirs, files), 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), ispath(q, ROOT_INO, m8, dirs, files), ispath(p0, ROOT_INO, m9, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, m ∈ files, psynced → asynced ⊦ # links(m, dirs) = count(⌜m⌝ , root.fids), # links(⌜m⌝ , root) = 0, links(⌜m⌝ , root) = ∅, p0 = q, root[path].dir?, m ∈ dirs, m8 ∈ dirs, m9 ∈ dirs

Rule argument

Additional information

Used simplifier rules: 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-target: ⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files));%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);% ⊦ ¬ fnode(fid).dir?; (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)