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Proof step 11 from proof precise-mapornull (previous step)

⊦ (∅ ++ r)[r, o] = (∅ ++ r)[r, o0], r = null, r ∈ H, r ∈ H0, r ∈ (∅ ++ r)[r, o] ∪ H0, r ∈ (∅ ++ r)[r, o0] ∪ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1)

Rule argument

spec: heap name: in-uni seq: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1) subst: [H1, H0, r] → [H0, (∅ ++ r)[r, o], r] flags: <all paths>

Additional information

Used simplifier rules: r ≠ null ⊦ (∅ ++ r)[r, o] ⊥ H ↔ ¬ r ∈ H; (s)% ⊦ r ∈ H[r0, o] ↔ r ∈ H; (s)% ⊦ ¬ r ∈ ∅; (s)%r0 ≠ null, ¬ r0 ∈ H ⊦ r ∈ H ++ r0 ↔ r = r0 ∨ r ∈ H; (s) Used terms: H0, (∅ ++ r)[r, o], r