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Proof step 6 from proof map-in (previous step)

mk(rs, f) = H0 ∪ H, ((r => o))(H0), P(H), H0 ⊥ H ⊦ r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 8:
((r => o))(H0), P(H), H0 ⊥ H, ∀ r. (r ∈ mk(rs, f) ↔ r ∈ H0 ∪ H) ∧ (r ∈ mk(rs, f) → mk(rs, f)[r] = (H0 ∪ H)[r]) ⊦ r ∈ rs

Rule argument

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

Additional information

Used terms: H0 ∪ H, mk(rs, f)