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Proof step 4 from proof path-split-wand (previous step)

p ∈ tree ⊦ abs(tree, ino0)(dirs) ↔ (_∃(λ ino1. abs(tree[p], ino1) * (abs(tree[p], ino1) -* abs(tree, ino0))))(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
p ∈ tree ⊦ abs(tree, ino0)(dirs) ↔ (∃ ino. ((abs(tree[p], ino) * (abs(tree[p], ino) -* abs(tree, ino0))))(dirs))

Rule argument

Additional information

Used simplifier rules: ⊦ (_∃ nD)(dirs) ↔ (∃ ino. nD(ino)(dirs)); (s)