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Proof step 199 from proof refine-mkdir (previous step)

dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs, files), of-cons(of, dirs0, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino1 ∈ dirs0, ino2 ∈ dirs4, dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], dirs4 ≡ dirs3 ++ ino2, dirs ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], psynced → asynced0 ⊦ # links(ino1, dirs0) = 0, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, pre-mkdir(q + str ', md, ESUCCESS, user, root, abs-files(files), abs-of(of)), ino2 ∈ dirs3, ino1 ∈ dirs, str ∈ entries0, ino2 ∈ files, ino2 ∈ dirs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 200:
⊦ pre-mkdir(p, md, ESUCCESS, user, root, fs, ofh) ↔ ¬ p ∈ root ∧ parent(p) ∈ root ∧ root[parent(p)].dir? ∧ py(user, parent(p), root, fs)
Proof step 201:
dirs0[ino1] = mkdir(# entries0, md1, # links(ino1, dirs0), m1, entries0), ((ino2 => mkdir(0, md, 1, 0, ∅) * (λ dirs1. dirs3 = dirs1)))(dirs), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px-parent(user, q, ROOT_INO, dirs0, files), ino2 ∈ dirs4, ino1 ∈ dirs0, dirs ≡ dirs4[ino2, mkdir(0, md, 1, 0, ∅)], dirs4 ≡ dirs3 ++ ino2, dirs3 ≡ dirs0[ino1, mkdir(# entries0 + 1, md1, # links(ino1, dirs0), m1 + 1, entries0[str, ino2])], psynced → asynced0 ⊦ # links(ino1, dirs0) = 0, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, ino2 ∈ dirs0, ino2 ∈ files, str ∈ entries0, ino1 ∈ dirs, ino2 ∈ dirs3, ¬ q + str ' ∈ root ∧ parent(q + str ') ∈ root ∧ root[parent(q + str ')].dir? ∧ py(user, parent(q + str '), root, abs-files(files))

Rule argument

spec: posix-pre name: pre-mkdir-esuccess seq: ⊦ pre-mkdir(p, md, ESUCCESS, user, root, fs, ofh) ↔ ¬ p ∈ root ∧ parent(p) ∈ root ∧ root[parent(p)].dir? ∧ py(user, parent(p), root, fs) subst: [ofh, fs, root, user, md, p] → [abs-of(of), abs-files(files), root, user, md, q + str '] flags: <all paths>

Additional information

Used terms: abs-of(of), abs-files(files), root, user, md, q + str '