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Proof step 43 from proof inv-fsync (previous step)

⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), # links(ino0, dirs) = m1, files[ino0] = mkfile(m, md, m1, content), files[ino0] = mkfile(m0, md0, m1, content0), err = ESUCCESS, ino1 = ROOT_INO, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true, ino0 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), files[ino0] = mkfile(m0, md0, # links(ino0, dirs), content0), err = ESUCCESS, ino1 = ROOT_INO, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, md0), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files, ¬ ino0 ∈ dirs ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)