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Proof step 21 from proof lst-in-hp (previous step)

H0 = (∅ ++ r)[r, a × r0], mk(rs1, cf) = H0 ∪ H, rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r0, x0)(H), H0 ⊥ H, ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs1, r ∈ rs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
mk(rs1, cf) = (∅ ++ r)[r, a × r0] ∪ H, rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r0, x0)(H), ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs0, r ∈ rs1, r ∈ H

Rule argument

Additional information

Used simplifier rules: r ≠ null ⊦ (∅ ++ r)[r, ce] ⊥ H ↔ ¬ r ∈ H; (s)