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Proof step 29 from proof payload-mod (previous step)

zbrar[m] = mkzentry(zbrar[(m + 1) + n0].key, adr0), payload(zbrar[(m + 1) + n0, mkzentry(zbrar[(m + 1) + n0].key, adr)], m + 1, nused0) = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr], n0 < nused0, m + nused0 < # zbrar, m < # zbrar, m + nused0 + 1 ≤ # zbrar, ∀ m0, m1. m0 < m1 ∧ m1 < nused0 + 1 → zbrar[m + m0].key < zbrar[m + m1].key ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr0] = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
zbrar[m] = mkzentry(zbrar[(m + 1) + n0].key, adr0), payload(zbrar[(m + 1) + n0, mkzentry(zbrar[(m + 1) + n0].key, adr)], m + 1, nused0) = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr], m < # zbrar, n0 < nused0, m + nused0 < # zbrar, ∀ m0, m1. m0 < m1 ∧ ¬ nused0 < m1 → zbrar[m + m0].key < zbrar[m + m1].key ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr0] = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)