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Proof step 93 from proof refine-readdir (previous step)

root[path] = dnode(md0, sdt), dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root.dir?, dom of < ino0, (_∃(λ ino1. abs|(root, ROOT_INO, path, ino1) * abs(root[path], ino1)))(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, path ∈ root, psynced → asynced ⊦ dom entries = dom sdt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 94:
root[path] = dnode(md0, sdt), dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), ((abs|(root, ROOT_INO, path, ino1) * abs(dnode(md0, sdt), ino1)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, path ∈ root, psynced → asynced ⊦ dom entries = dom sdt

Rule argument

Additional information

Used simplifier rules: absc-path: ⊦ p ∈ tree ∧ ((abs|(tree, ino, p, ino0) * D))(dirs) ∧ ispath(p, ino, ino1, dirs, files) → ino0 = ino1; (forward) from specification vfs-abs%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]% ⊦ (_∃ nD)(dirs) ↔ (∃ ino. nD(ino)(dirs)); (s)