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Proof step 37 from proof rely-owned-unchgd (previous step)

rs2 ∩ rs1 = ∅, P(mk(rs2, f)), ∀ r. r ∈ rs2 → g(r) = a, ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)) ⊦ mk(rs2, f0) = mk(rs2, f), P(mk(rs2, f0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 39:
rs2 ∩ rs1 = ∅, P(mk(rs2, f)), ∀ r. (g(r) = a ∧ r ∈ rs2 ∪ rs1 ↔ g0(r) = a ∧ r ∈ rs0) ∧ (g(r) = a ∧ r ∈ rs2 ∪ rs1 → f(r) = f0(r)), ∀ r. r ∈ rs2 → g(r) = a ⊦ P(mk(rs2, f0)), ∀ r. (r ∈ mk(rs2, f0) ↔ r ∈ mk(rs2, f)) ∧ (r ∈ mk(rs2, f0) → mk(rs2, f0)[r] = mk(rs2, f)[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(rs2, f), mk(rs2, f0)] flags: <all paths>

Additional information

Used terms: mk(rs2, f), mk(rs2, f0)