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Proof step 18 from proof path-split-wand (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ str ∈ sdt ↔ (∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0)
Proof step 20:
((ino0 => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)))(dirs), str ∈ entries, p0 ∈ sdt[str], ∀ tree, ino0, dirs. abs(tree, ino0)(dirs) ∧ p0 ∈ tree → (∃ ino. ((abs(tree[p0], ino) * (abs(tree[p0], ino) -* abs(tree, ino0))))(dirs)), ∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0 ⊦ ∃ ino. (( abs(sdt[str][p0], ino) * (abs(sdt[str][p0], ino) -* _∃(λ ad0. ino0 => ad0 * abs(sdt, ad0.entries) ∧ ⌜ad0.meta = md⌝ ∧ ⌜ad0.size = # ad0.entries⌝ ))) )(dirs)

Rule argument

spec: store, inst: directory-tree-inst name: exin seq: ⊦ str ∈ sdt ↔ (∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0) subst: [sdt, str] → [sdt, str] flags: <all paths>

Additional information

Used terms: sdt, str