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Proof step 31 from proof del-lists-unions (previous step)

P(H1), del-list(rx0, n0)(H), ls(r, x)(H2), H1 ⊥ H, H1 ⊥ H2, H2 ⊥ 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, # x ≤ n0 + # x ∧ (((ls(r, x) * del-list(rx0, n0 + # x - # x)) * P))((H2 ∪ H) ∪ H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
P(H1), del-list(rx0, n0)(H), ls(r, x)(H2), H2 ⊥ H, H1 ⊥ H2, 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: ⊦ m + n - m = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)