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Proof step 51 from proof inv-fsync (previous step)

⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err0)⟩ (ino1 = ino0 ∧ err0 = ESUCCESS), files[ino0] = mkfile(m0, md0, # links(ino0, dirs), content0), err0 = 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 ⊦ ⟪afs_sync#(dirs, files; ; asynced, err0)⟫ true

User applied rule call right

And obtained the following new goals

Proof step 52:
⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err0)⟩ (ino1 = ino0 ∧ err0 = ESUCCESS), files[ino0] = mkfile(m0, md0, # links(ino0, dirs), content0), err0 = 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 ⊦ ⟪fail_or_success#(; ; err); asynced := err = ESUCCESS⟫ true, ino0 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_sync#(DIRS, FILES; ; ASYNCED, ERR) {fail_or_success#(; ; ERR); ASYNCED := ERR = ESUCCESS};