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Proof step 9 from proof payload-split (previous step)

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)

User applied rule all left

And obtained the following new goals

Proof step 10:
m + n0 + n1 < # zbrar, m < # zbrar, (m + 1) + n0 + n1 ≤ # zbrar → payload(zbrar, m + 1, n0 + n1) = payload(zbrar, m + 1, n1) ⊕ payload(zbrar, (m + 1) + 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

pos: left 3 terms: m + 1, n0, zbrar abort: F discard: T computed: F

Additional information

Used terms: m + 1, n0, zbrar