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Proof step 6 from proof map-write (previous step)

H[r, o1] = (∅ ++ r)[r, o0] ∪ H0, P(H0), r ∈ H ⊦ o0 = o1, r ∈ H0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 8:
P(H0), r ∈ H, ∀ r0. (r0 ∈ H[r, o1] ↔ r0 ∈ (∅ ++ r)[r, o0] ∪ H0) ∧ (r0 ∈ H[r, o1] → H[r, o1][r0] = ((∅ ++ r)[r, o0] ∪ H0)[r0]) ⊦ o0 = o1, r ∈ H0

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [(∅ ++ r)[r, o0] ∪ H0, H[r, o1]] flags: <all paths>

Additional information

Used terms: (∅ ++ r)[r, o0] ∪ H0, H[r, o1]