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Proof step 25 from proof mod-other-both (previous step)

rs1 ∩ rs0 = ∅, P(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ g(r) = a, mk(rs1, f(r; o)) = mk(rs1, f), P(mk(rs1, f(r; o))), (a[P] * true)[rs1 ∪ rs0, f(r; o), g(r; a0)], r ∈ rs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[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(rs1, f), mk(rs1, f(r; o))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ r ∈ mk(rs, f) ↔ r ∈ rs; (s)% ⊦ r ∈ rs → mk(rs, f)[r] = f(r); (s) Used terms: mk(rs1, f), mk(rs1, f(r; o))