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Proof step 27 from proof lift-emp (previous step)

∀ r0. ¬ r0 ∈ rs ⊦ mk(rs, f) = ∅, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 29:
∀ r0. ¬ r0 ∈ rs ⊦ r ∈ rs, ∀ r. (r ∈ mk(rs, f) ↔ r ∈ ∅) ∧ (r ∈ mk(rs, f) → mk(rs, f)[r] = (∅)[r])

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [∅, mk(rs, f)] flags: <all paths>

Additional information

Used terms: ∅, mk(rs, f)