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Proof step 48 from proof refine-readmeta (previous step)

dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), root[path].dir?, 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, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ dirs, psynced → asynced ⊦ pre-readmeta(path, ESUCCESS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then if root[path].dir? then md := root[path].meta, ino0 := # root[path].subdirs + 2, ino := # root[path].entries else let fid = root[path].fid in md := abs-files(files)[fid].meta, ino0 := count(fid, root.fids), ino := # abs-files(files)[fid].content⟩ ((psynced → asynced) ∧ md1 = md ∧ m2 + 2 = ino0 ∧ # entries = ino ∧ ESUCCESS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 50:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (pr(user, p, tree, abs-files(files)) ↔ pr(user, meta(ε, m, dirs, files)))
Proof step 51:
dirs[m] = mkdir(# entries, md1, # links(m, dirs), m2, entries), root[path].dir?, 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, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ dirs, psynced → asynced ⊦ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then if root[path].dir? then md := root[path].meta, ino0 := # root[path].subdirs + 2, ino := # root[path].entries else let fid = root[path].fid in md := abs-files(files)[fid].meta, ino0 := count(fid, root.fids), ino := # abs-files(files)[fid].content⟩ ((psynced → asynced) ∧ md1 = md ∧ m2 + 2 = ino0 ∧ # entries = ino ∧ ESUCCESS = err0)

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));%pr: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( pr(user, p, tree, abs-files(files)) ↔ pr(user, meta(ε, m, dirs, files)));% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%⊦ pre-readmeta(p, ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ pr(user, p, root, fs); (s)