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Proof step 20 from proof path-unfold (previous step)

(((ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)) * D))(dirs), p0 ∈ sdt[str], str ∈ sdt, str ∈ entries, ∀ tree, ino0, D, dirs. ((abs(tree, ino0) * D))(dirs) ∧ p0 ∈ tree → (∃ ino. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(dirs)) ⊦ ∃ ino, ad0. str ∈ ad0.entries ∧ ad0.meta = md ∧ ad0.size = # ad0.entries ∧ (((((abs|(sdt[str], ad0.entries[str], p0, ino) * abs(sdt -- str, ad0.entries -- str)) * ino0 => ad0) * abs(sdt[str][p0], ino)) * D))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ str ∈ sdt → abs(sdt, sdi) = (⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str]))
Proof step 22:
(((ino0 => mkdir(# entries, md, m0, m1, entries) * (⌜str ∈ entries⌝ ∧ abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str]))) * D) )(dirs), str ∈ entries, p0 ∈ sdt[str], str ∈ sdt, ∀ tree, ino0, D, dirs. ((abs(tree, ino0) * D))(dirs) ∧ p0 ∈ tree → (∃ ino. (((abs|(tree, ino0, p0, ino) * abs(tree[p0], ino)) * D))(dirs)) ⊦ ∃ ino, ad0. str ∈ ad0.entries ∧ ad0.meta = md ∧ ad0.size = # ad0.entries ∧ (((((abs|(sdt[str], ad0.entries[str], p0, ino) * abs(sdt -- str, ad0.entries -- str)) * ino0 => ad0) * abs(sdt[str][p0], ino)) * D))(dirs)

Rule argument

spec: <toplevel> name: entries-recdel seq: ⊦ str ∈ sdt → abs(sdt, sdi) = ( ⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str])) subst: [str, sdi, sdt] → [str, entries, sdt] flags: <all paths>

Additional information

Used terms: str, entries, sdt