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Proof step 25 from proof del-lists-unions (previous step)

(((ls(r, x0) * del-list(rx0, n1)) * P))(H2 ∪ H ∪ H1), del-list(rx0, n0)(H), ls(r, x)(H2), H1 ⊥ H2, H2 ⊥ H, H1 ⊥ H, ∀ n, H0, H1, m, P. del-list(rx0, n)(H0) ∧ H0 ⊥ H1 → (((del-list(rx0, m) * P))(H0 ∪ H1) ↔ n = m ∧ P(H1)) ⊦ r = null, H2 ⊥ H ∪ H1, n0 + # x = n1 + # x0 ∧ P(H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ H1 ⊥ H → (H0 ⊥ H1 ∪ H ↔ H0 ⊥ H1 ∧ H0 ⊥ H)

Rule argument

spec: heap, inst: cell-heap name: disj-distr-uni seq: ⊦ H1 ⊥ H → (H0 ⊥ H1 ∪ H ↔ H0 ⊥ H1 ∧ H0 ⊥ H) subst: [H, H1, H0] → [H1, H, H2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H1, H, H2