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Proof step 19 from proof lst-in-hp (previous step)

mk(rs1, cf) = H0 ∪ H, rs1 ∩ rs0 = ∅, ((r => a × r0))(H0), R[rs0, cf, af], ls(r0, x0)(H), H0 ⊥ H, ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs0, r ∈ rs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ((r => ce))(H) ↔ H = (∅ ++ r)[r, ce] ∧ r ≠ null
Proof step 21:
H0 = (∅ ++ r)[r, a × r0], mk(rs1, cf) = H0 ∪ H, rs1 ∩ rs0 = ∅, R[rs0, cf, af], ls(r0, x0)(H), H0 ⊥ H, ∀ r. r ∈ rs1 → af(r) = o ⊦ r = null, r ∈ rs1, r ∈ rs0

Rule argument

spec: maplet, inst: cell-heap-aux name: maplet seq: ⊦ ((r => ce))(H) ↔ H = (∅ ++ r)[r, ce] ∧ r ≠ null subst: [H, ce, r] → [H0, a × r0, r] flags: <all paths>

Additional information

Used terms: H0, a × r0, r