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Proof step 146 from proof refine-readmeta (previous step)

dirs[m9] = mkdir(# entries, md, # links(m9, dirs), m4, entries), root[q + str '] = fnode(⌜m⌝ ), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), files[m] = mkfile(m0, md1, # links(m, dirs), content), root.dir?, root[q].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, m9, dirs, files), ispath(path, ROOT_INO, m, dirs, files), ispath(q + str ', ROOT_INO, m8, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m9 ∈ dirs, ROOT_INO ∈ dirs, m ∈ files, str ' ∈ root[q], psynced → asynced ⊦ # links(m, dirs) = count(⌜m⌝ , root.fids), # links(⌜m⌝ , root) = 0, links(⌜m⌝ , root) = ∅, root[path].dir?, m ∈ dirs, m8 ∈ dirs, m = entries[str] ∧ str ∈ entries

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 147:
⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files))
Proof step 148:
files[m] = mkfile(m0, md1, # links(m, dirs), content), dirs[m1] = mkdir(m5, md0, m6, m7, entries0), root[q + str '] = fnode(⌜m⌝ ), dirs[m9] = mkdir(# entries, md, # links(m9, dirs), m4, entries), root[q].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), ispath(q, ROOT_INO, m9, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), str ' ∈ root[q], m ∈ files, ROOT_INO ∈ dirs, m9 ∈ dirs, psynced → asynced, ∃ m0. ispath(q, ROOT_INO, m0, dirs, files) ∧ ispath(str ', m0, m8, dirs, files) ⊦ # links(⌜m⌝ , root) = 0, # links(m, dirs) = count(⌜m⌝ , root.fids), links(⌜m⌝ , root) = ∅, root[path].dir?, m8 ∈ dirs, m ∈ dirs, m = entries[str] ∧ str ∈ entries

Rule argument

spec: afs-base name: path-split seq: ⊦ ispath(p + q, n, m, dirs, files) ↔ (∃ m0. ispath(p, n, m0, dirs, files) ∧ ispath(q, m0, m, dirs, files)) subst: [files, dirs, m, n, q, p] → [files, dirs, m8, ROOT_INO, str ', q] flags: <all paths>

Additional information

Used terms: files, dirs, m8, ROOT_INO, str ', q