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Proof step 10 from proof exin-uni (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: uni-write seq: r ≠ null, r ∈ H1, H0 ⊥ H1 ⊦ H0 ∪ H1[r, o] = (H0 ∪ H1)[r, o] subst: [o, r, H1, H0] → [o, r, ∅ ++ r, H0] flags: <all paths>

Additional information

Used simplifier rules: nonnull: ⊦ r ∈ H → r ≠ null;%in-emp: ⊦ ¬ r ∈ ∅;%disj-r: ⊦ r ∈ H1 ∧ H0 ⊥ H1 → (r ∈ H0 ↔ false);%disj-emp-r: ⊦ H ⊥ ∅;%uni-alloc: r ≠ null, ¬ r ∈ H1, ¬ r ∈ H0, H0 ⊥ H1 ⊦ H0 ∪ (H1 ++ r) = (H0 ∪ H1) ++ r;%uni-emp-r: ⊦ H ∪ ∅ = H; Used terms: o, r, ∅ ++ r, H0