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Proof step 15 from proof sep (previous step)

mk(rs, f) = mk(rs0, f0) ∪ mk(rs1, f1), rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)) ⊦ rs0 ∪ rs1 = rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 17:
rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)), ∀ r. (r ∈ mk(rs, f) ↔ r ∈ mk(rs0, f0) ∪ mk(rs1, f1)) ∧ (r ∈ mk(rs, f) → mk(rs, f)[r] = (mk(rs0, f0) ∪ mk(rs1, f1))[r]) ⊦ rs0 ∪ rs1 = rs

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [mk(rs0, f0) ∪ mk(rs1, f1), mk(rs, f)] flags: <all paths>

Additional information

Used terms: mk(rs0, f0) ∪ mk(rs1, f1), mk(rs, f)