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Proof step 5 from proof path-unfold (previous step)

p ∈ tree ⊦ ∀ D1, dirs. ((abs(tree, ino0) * D1))(dirs) ↔ ((_∃(λ ino1. abs|(tree, ino0, p, ino1) * abs(tree[p], ino1)) * D1))(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
p ∈ tree ⊦ ((abs(tree, ino0) * D))(dirs) ↔ (∃ ino. (((abs|(tree, ino0, p, ino) * abs(tree[p], ino)) * D))(dirs))

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]% ⊦ ((_∃ nD * D))(dirs) ↔ (∃ ino. ((nD(ino) * D))(dirs)); (s)