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Proof step 27 from proof lst-in-hp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1)

Rule argument

spec: heap, inst: cell-heap-aux name: in-uni seq: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1) subst: [H1, H0, r] → [H, (∅ ++ r)[r, a × r0], r] flags: <all paths>

Additional information

Used simplifier rules: r ≠ null ⊦ (∅ ++ r)[r, ce] ⊥ H ↔ ¬ r ∈ H; (s)% ⊦ r ∈ H[r0, ce] ↔ r ∈ H; (s)% ⊦ ¬ r ∈ ∅; (s)%r0 ≠ null, ¬ r0 ∈ H ⊦ r ∈ H ++ r0 ↔ r = r0 ∨ r ∈ H; (s) Used terms: H, (∅ ++ r)[r, a × r0], r