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Proof step 10 from proof mapex-new (previous step)

P(H) ⊦ H ++ r = (∅ ++ r)[r, (H ++ r)[r]] ∪ H, r = null, r ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 12:
P(H) ⊦ r = null, r ∈ H, ∀ r0. (r0 ∈ H ++ r ↔ r0 ∈ (∅ ++ r)[r, (H ++ r)[r]] ∪ H) ∧ (r0 ∈ H ++ r → (H ++ r)[r0] = ((∅ ++ r)[r, (H ++ r)[r]] ∪ H)[r0])

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, (H ++ r)[r]] ∪ H, H ++ r] flags: <all paths>

Additional information

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