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Proof step 8 from proof payload-split (previous step)

m + n0 + n1 < # zbrar, m < # zbrar, ∀ m, n0, zbrar. m + n0 + n1 ≤ # zbrar → payload(zbrar, m, n0 + n1) = payload(zbrar, m, n1) ⊕ payload(zbrar, m + n1, n0) ⊦ # zbrar = 0, (zbrar[m].entry? ⊃ payload(zbrar, m + 1, n1 + n0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, n1 + n0)) = payload(zbrar, m, n1 + 1) ⊕ payload(zbrar, m + n1 + 1, n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m < # zbrar, m + n0 + n1 < # zbrar, ∀ m, n0, zbrar. m + n0 + n1 ≤ # zbrar → payload(zbrar, m, n0 + n1) = payload(zbrar, m, n1) ⊕ payload(zbrar, m + n1, n0) ⊦ # zbrar = 0, (zbrar[m].entry? ⊃ payload(zbrar, m + 1, n1 + n0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, n1 + n0)) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, n1)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, n1)) ⊕ payload(zbrar, m + n1 + 1, n0)

Rule argument

Additional information

Used simplifier rules: payload-rec: ⊦ m < # zbrar → payload(zbrar, m, nused + 1) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused)[zbrar[m].key, zbrar[m].adr] ;payload(zbrar, m + 1, nused) );%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2