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Proof step 24 from proof path-split-wand (previous step)

(((abs(tree, entries[str]) * abs(sdt0, entries -- str)) * ino0 => mkdir(# entries, md, m0, m1, entries)))(dirs), p0 ∈ tree, ∀ tree, ino0, dirs. abs(tree, ino0)(dirs) ∧ p0 ∈ tree → (∃ ino. ((abs(tree[p0], ino) * (abs(tree[p0], ino) -* abs(tree, ino0))))(dirs)), ∃ ino, entries0. entries = entries0[str, ino] ∧ ¬ str ∈ entries0 ⊦ str ∈ sdt0, ∃ ino. (( abs(tree[p0], ino) * ( abs(tree[p0], ino) -* _∃ (λ ad. (⌜str ∈ ad.entries⌝ ∧ (abs(tree, ad.entries[str]) * abs(sdt0, ad.entries -- str)) * ino0 => ad) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ))) )(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
((abs(tree, ino) * abs(sdt0, entries0) * ino0 => mkdir(# entries0 + 1, md, m0, m1, entries0[str, ino])))(dirs), p0 ∈ tree, ∀ tree, ino0, dirs. abs(tree, ino0)(dirs) ∧ p0 ∈ tree → (∃ ino. ((abs(tree[p0], ino) * (abs(tree[p0], ino) -* abs(tree, ino0))))(dirs)) ⊦ str ∈ sdt0, str ∈ entries0, ∃ ino. (( abs(tree[p0], ino) * ( abs(tree[p0], ino) -* _∃ (λ ad. (⌜str ∈ ad.entries⌝ ∧ (abs(tree, ad.entries[str]) * abs(sdt0, ad.entries -- str)) * ino0 => ad) ∧ ⌜ad.meta = md⌝ ∧ ⌜ad.size = # ad.entries⌝ ))) )(dirs)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ str ∈ entries → # entries[str, ino] = # entries + 1; (s)% ⊦ ¬ str ∈ entries → entries -- str = entries; (s)% ⊦ entries[str, ino] -- str = entries -- str; (s)% ⊦ entries[str, ino][str] = ino; (s)