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Proof step 31 from proof cf-map-unknown (previous step)

cf(r) = a × r0, rs1 ∩ rs0 = ∅, ((r => ce))(mk(rs1, cf)), 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 32:
⊦ ((r => ce))(H) ↔ H = (∅ ++ r)[r, ce] ∧ r ≠ null
Proof step 33:
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]))

Rule argument

spec: maplet, inst: cell-heap-aux name: maplet seq: ⊦ ((r => ce))(H) ↔ H = (∅ ++ r)[r, ce] ∧ r ≠ null subst: [H, ce, r] → [mk(rs1, cf), ce, r] flags: <all paths>

Additional information

Used terms: mk(rs1, cf), ce, r