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Proof step 15 from proof mk-exists (previous step)

∀ H1. # H1 < # (mk(rs, f) ++ r)[r, o] → true → (∃ rs, f. H1 = mk(rs, f)) ⊦ (mk(rs, f) ++ r)[r, o] = mk(rs ++ r, f(r; o)), r = null, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 17:
∀ H1. # H1 < # (mk(rs, f) ++ r)[r, o] → true → (∃ rs, f. H1 = mk(rs, f)) ⊦ r = null, r ∈ rs, ∀ r0. (r0 ∈ (mk(rs, f) ++ r)[r, o] ↔ r0 ∈ mk(rs ++ r, f(r; o))) ∧ (r0 ∈ (mk(rs, f) ++ r)[r, o] → (mk(rs, f) ++ r)[r, o][r0] = mk(rs ++ r, f(r; o))[r0])

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [mk(rs ++ r, f(r; o)), (mk(rs, f) ++ r)[r, o]] flags: <all paths>

Additional information

Used terms: mk(rs ++ r, f(r; o)), (mk(rs, f) ++ r)[r, o]