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Proof step 34 from proof cf-map-unknown (previous step)

cf(r) = a × r0, mk(rs1, cf) = (∅ ++ r)[r, ce], rs1 ∩ rs0 = ∅, R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], (r1 ∈ rs1 ↔ r1 = r) ∧ (r1 ∈ rs1 → cf(r1) = (r1 = r ⊃ a × r0;(∅ ++ r)[r1]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 36:
cf(r) = a × r0, rs1 ∩ rs0 = ∅, R[rs0, cf, af], ∀ r. r ∈ rs1 → af(r) = o, ∀ r0. (r0 ∈ mk(rs1, cf) ↔ r0 ∈ (∅ ++ r)[r, ce]) ∧ (r0 ∈ mk(rs1, cf) → mk(rs1, cf)[r0] = (∅ ++ r)[r, ce][r0]) ⊦ r = null, (o[r => a × r0] * R)[rs1 ∪ rs0, cf, af], (r1 ∈ rs1 ↔ r1 = r) ∧ (r1 ∈ rs1 → cf(r1) = (r1 = r ⊃ a × r0;(∅ ++ r)[r1]))

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, ce], mk(rs1, cf)] flags: <all paths>

Additional information

Used terms: (∅ ++ r)[r, ce], mk(rs1, cf)