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Proof step 34 from proof del-lists-unions (previous step)

P(H1), del-list(rx0, n0)(H), ls(r, x)(H2), H1 ⊥ H, H2 ⊥ H, H ⊥ H1, H1 ⊥ H2, ∀ 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, (((ls(r, x) * del-list(rx0, n0)) * P))(H2 ∪ H ∪ H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
P(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, (((ls(r, x) * del-list(rx0, n0)) * P))(H2 ∪ H ∪ H1)

Rule argument

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s)