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Proof step 41 from proof path-unfold (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: ⊦ ⌜true⌝ = true; (s)% ⊦ (true ∧ D) = D; (s)%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]%and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap] Used terms: str, entries, sdt