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Proof step 41 from proof refine-readmeta (previous step)

root.dir?, root[path].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, dirs[m].meta), px-parent(user, path, ROOT_INO, dirs, files), m ∈ dirs, psynced → asynced ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ dirs[m].meta = md0 ∧ dirs[m].nsubdirs + 2 = ino4 ∧ dirs[m].size = ino3 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
dirs[m] = mkdir(m0, md, m1, 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, md), px-parent(user, path, ROOT_INO, dirs, files), m ∈ dirs, psynced → asynced ⊦ ⟨posix_readmeta#(path, user, root, abs-files(files), abs-of(of); md0, ino4, ino3, err0)⟩ ((psynced → asynced) ∧ md = md0 ∧ m2 + 2 = ino4 ∧ m0 = ino3 ∧ ESUCCESS = err0)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md, m1, m2, entries