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Proof step 4 from proof payload-drop-lower (previous step)

m + n + nused0 +1 ≤ # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ n = 0, payload(zbrar[m, zbr], m + n, nused0 +1) = payload(zbrar, m + n, nused0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m + n + nused0 < # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ n = 0, payload(zbrar[m, zbr], m + n, nused0 + 1) = payload(zbrar, m + n, nused0 + 1)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)