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Proof step 27 from proof del-lists-unions (previous step)

x = x0, ((P * del-list(rx0, n1)))(H ∪ H1), del-list(rx0, n0)(H), ls(r, x)(H2), H1 ⊥ H, H2 ⊥ H, H1 ⊥ H2, H2 ⊥ H ∪ H1, ∀ 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, n0 + # x = n1 + # x0 ∧ P(H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
((P * del-list(rx0, n1)))(H ∪ H1), del-list(rx0, n0)(H), ls(r, x0)(H2), H2 ⊥ H ∪ H1, 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, n0 = n1 ∧ P(H1)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)