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Proof step 23 from proof sep (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 25:
mk(rs, f) = mk(rs0, f0) ∪ mk(rs1, f1), rs0 ∩ rs1 = ∅, P0(mk(rs0, f0)), P1(mk(rs1, f1)) ⊦ P0(mk(rs0, f)), ∀ r. (r ∈ mk(rs0, f) ↔ r ∈ mk(rs0, f0)) ∧ (r ∈ mk(rs0, f) → mk(rs0, f)[r] = mk(rs0, f0)[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(rs0, f0), mk(rs0, f)] flags: <all paths>

Additional information

Used terms: mk(rs0, f0), mk(rs0, f)