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Proof step 22 from proof lift-emp (previous step)

mk(rs, f, g) = ∅ ⊦ mk(rs, f) = ∅ ∧ (r ∈ rs → g(r) = a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ Ha0 = Ha1 ↔ (∀ r. (r ∈ Ha0 ↔ r ∈ Ha1) ∧ (r ∈ Ha0 → Ha0[r]o = Ha1[r]o ∧ Ha0[r]a = Ha1[r]a))
Proof step 24:
∀ r. (r ∈ mk(rs, f, g) ↔ r ∈ ∅) ∧ (r ∈ mk(rs, f, g) → mk(rs, f, g)[r]o = (∅)[r]o ∧ mk(rs, f, g)[r]a = (∅)[r]a) ⊦ mk(rs, f) = ∅ ∧ (r ∈ rs → g(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)] flags: <all paths>

Additional information

Used terms: ∅, mk(rs, f, g)