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Proof step 22 from proof lst-in-hp (previous step)

mk(rs1, cf) = (∅ ++ r)[r, a × r0] ∪ H, rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r0, x0)(H), ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs0, r ∈ rs1, r ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 24:
rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r0, x0)(H), ∀ r. r ∈ rs1 → af(r) = o, ∀ r1. (r1 ∈ mk(rs1, cf) ↔ r1 ∈ (∅ ++ r)[r, a × r0] ∪ H) ∧ (r1 ∈ mk(rs1, cf) → mk(rs1, cf)[r1] = ((∅ ++ r)[r, a × r0] ∪ H)[r1]) ⊦ r = null, r ∈ H, r ∈ rs1, r ∈ rs0

Rule argument

spec: heap, inst: cell-heap-aux name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [(∅ ++ r)[r, a × r0] ∪ H, mk(rs1, cf)] flags: <all paths>

Additional information

Used terms: (∅ ++ r)[r, a × r0] ∪ H, mk(rs1, cf)