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Proof step 23 from proof abs-unfold (previous step)

tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(# entries, md, # links(ino, dirs), m1, entries) * abs(sdt, entries)))(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), p ∈ tree ⊦ ((abs|(tree, ROOT_INO, p, ino) * abs(dnode(md, sdt), ino)))(dirs), abs(tree0, ROOT_INO)(dirs0), ∃ ino. ((abs|(tree, ROOT_INO, p, ino) * abs(dnode(md, sdt), ino)))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ abs(dnode(md, sdt), ino) = _∃(λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ )
Proof step 25:
tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino) * ino => mkdir(# entries, md, # links(ino, dirs), m1, entries) * abs(sdt, entries)))(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), p ∈ tree ⊦ ((abs|(tree, ROOT_INO, p, ino) * _∃(λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ )))(dirs), abs(tree0, ROOT_INO)(dirs0), ∃ ino. ((abs|(tree, ROOT_INO, p, ino) * abs(dnode(md, sdt), ino)))(dirs)

Rule argument

spec: vfs-abs name: abs-dnode seq: ⊦ abs(dnode(md, sdt), ino) = _∃ (λ ad. ino => ad * abs(sdt, ad.entries) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ) subst: [ino, sdt, md] → [ino, sdt, md] flags: <all paths>

Additional information

Used terms: ino, sdt, md