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Proof step 3 from proof del-lists-unions (previous step)

del-list(r + rx0, n)(H0), H0 ⊥ H1, ∀ n, H0, H1, m, P. del-list(rx0, n)(H0) ∧ H0 ⊥ H1 → (((del-list(rx0, m) * P))(H0 ∪ H1) ↔ n = m ∧ P(H1)) ⊦ ((del-list(r + rx0, m) * P))(H0 ∪ H1) ↔ n = m ∧ P(H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
del-list(r ' + rx0, n)(H0), H0 ⊥ H1, ∀ n, H0, H1, m, P. del-list(rx0, n)(H0) ∧ H0 ⊥ H1 → (((del-list(rx0, m) * P))(H0 ∪ H1) ↔ n = m ∧ P(H1)) ⊦ ((del-list(r ' + rx0, m) * P))(H0 ∪ H1) ↔ n = m ∧ P(H1)

Rule argument

Additional information

Used simplifier rules: ⊦ r + rx = r ' + rx; (s)