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Proof step 13 from proof sw-del-add-new (previous step)

r0 ∈ H, r0 ∈ (H ++ r)[r, o] ⊦ (H ++ r)[r, o][r0] = H[r0], r = null, r ∈ rs, r ∈ H, r0 ∈ rs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
r0 ∈ H ⊦ (H ++ r)[r0] = H[r0], r = null, r0 ∈ rs, r ∈ H, r ∈ rs

Rule argument

Additional information

Used simplifier rules: at-write: ⊦ H[r0, o][r] = (r = r0 ∧ r0 ∈ H ⊃ o;H[r]);%in-write: ⊦ r ∈ H[r0, o] ↔ r ∈ H;%in-alloc: r0 ≠ null, ¬ r0 ∈ H ⊦ r ∈ H ++ r0 ↔ r = r0 ∨ r ∈ H;