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Proof step 3 from proof alloc (previous step)

⊦ R[rs, f, g] ↔ (a[r =>_] * R)[rs ++ r, f, g(r; a)], r = null, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
¬ r ∈ rs, r ≠ null ⊦ R[rs, f, g] ↔ (r ==>_ * R)[rs ++ r, f, g]
Proof step 5:
⊦ (r ==>_ * R)[rs ++ r, f, g] ↔ (a[r =>_] * R)[rs ++ r, f, g(r; a)], r = null, r ∈ rs

Rule argument

spec: heap-fun, inst: heap-aux name: mapex-new seq: ¬ r ∈ rs, r ≠ null ⊦ R[rs, f, g] ↔ (r ==>_ * R)[rs ++ r, f, g] subst: [r, g, f, rs, R] → [r, g, f, rs, R] flags: <all paths>

Additional information

Used terms: r, g, f, rs, R