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Proof step 6 from proof path-unfold-wand (previous step)

abs|(tree, ino0, p, ino1)(dirs), p ∈ tree ⊦ ((abs(tree[p], ino1) -* abs(tree, ino0)))(dirs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ((D -* D0))(dirs) ↔ (∀ dirs0. dirs0 ⊥ dirs ∧ D(dirs0) → D0(dirs0 ∪ dirs))
Proof step 8:
abs|(tree, ino0, p, ino1)(dirs), p ∈ tree ⊦ ∀ dirs0. dirs0 ⊥ dirs ∧ abs(tree[p], ino1)(dirs0) → abs(tree, ino0)(dirs0 ∪ dirs)

Rule argument

spec: heap-sep, inst: dir-heap name: wand seq: ⊦ ((D -* D0))(dirs) ↔ (∀ dirs0. dirs0 ⊥ dirs ∧ D(dirs0) → D0(dirs0 ∪ dirs)) subst: [dirs, D0, D] → [dirs, abs(tree, ino0), abs(tree[p], ino1)] flags: <all paths>

Additional information

Used terms: dirs, abs(tree, ino0), abs(tree[p], ino1)