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Proof step 2 from proof tr-unfold (previous step)

⊦ ((tr(r, t) * P))(H) ↔ (∃ t0, t1, a, r0, r1. t = branch(t0, a, t1) ∧ ((r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P))(H)), r = null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
((tr(r, t) * P))(H) ⊦ r = null, ∃ t0, t1, a, r0, r1. t = branch(t0, a, t1) ∧ ((r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P))(H)

Rule argument

Additional information

Used simplifier rules: tr-fold: ⊦ ((r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P))(H) → ((tr(r, branch(t0, a, t1)) * P))(H);%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep