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Proof step 8 from proof switch-obj (previous step)

⊦ R(mk(rs, f(r; o), g)) ↔ R(mk(rs, f, g)), mk(rs, f(r; o), g) = mk(rs, f, g), r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ Ha0 = Ha1 ↔ (∀ r. (r ∈ Ha0 ↔ r ∈ Ha1) ∧ (r ∈ Ha0 → Ha0[r]o = Ha1[r]o ∧ Ha0[r]a = Ha1[r]a))

Rule argument

spec: heap, inst: heap-aux name: ext seq: ⊦ Ha0 = Ha1 ↔ (∀ r. (r ∈ Ha0 ↔ r ∈ Ha1) ∧ (r ∈ Ha0 → Ha0[r]o = Ha1[r]o ∧ Ha0[r]a = Ha1[r]a)) subst: [Ha1, Ha0] → [mk(rs, f, g), mk(rs, f(r; o), g)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ r ∈ mk(rs, f, g) ↔ r ∈ rs; (s)% ⊦ r ∈ rs → mk(rs, f, g)[r]o = f(r); (s)% ⊦ r ∈ rs → mk(rs, f, g)[r]a = g(r); (s) Used terms: mk(rs, f, g), mk(rs, f(r; o), g)