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Proof step 3 from proof path-unfold (previous step)

p ∈ tree ⊦ abs(tree, ino0) = _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ D = D0 ↔ (∀ D1, dirs. ((D * D1))(dirs) ↔ ((D0 * D1))(dirs))
Proof step 5:
p ∈ tree ⊦ ∀ D1, dirs. ((abs(tree, ino0) * D1))(dirs) ↔ ((_∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)) * D1))(dirs)

Rule argument

spec: heap-sep, inst: dir-heap name: Eq-P seq: ⊦ D = D0 ↔ (∀ D1, dirs. ((D * D1))(dirs) ↔ ((D0 * D1))(dirs)) subst: [D0, D] → [_∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)), abs(tree, ino0)] flags: <all paths>

Additional information

Used terms: _∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)), abs(tree, ino0)