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Proof step 12 from proof abs-fold-del-p (previous step)

# entries = m + 1, tree[p] = dnode(md, sdt), ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(m, md, m0, m1, entries -- str) * abs(sdt -- str, entries -- str) * D))(dirs), p ∈ tree, str ∈ entries ⊦ entries = ∅, (((abs|(tree[p, dnode(md, sdt -- str)], ROOT_INO, p, ino0) * abs(dnode(md, sdt -- str), ino0)) * D))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [ino0, sdt -- str, md] flags: <all paths>

Additional information

Used terms: ino0, sdt -- str, md