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Proof step 18 from proof payload-mod (previous step)

n0 < nused0, m + nused0 < # zbrar, m < # zbrar, sorted(zbrar, m, nused0 + 1), ∀ n, zbrar, m, adr. n < nused0 ∧ sorted(zbrar, m, nused0) ∧ m + nused0 ≤ # zbrar → payload(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0) = payload(zbrar, m, nused0)[zbrar[m + n].key, adr] ⊦ (zbrar[m].entry? ⊃ payload(zbrar[m + n0 + 1, mkzentry(zbrar[m + n0 + 1].key, adr)], m + 1, nused0)[zbrar[m].key, zbrar[m].adr] ;payload(zbrar[m + n0 + 1, mkzentry(zbrar[m + n0 + 1].key, adr)], m + 1, nused0) ) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0))[zbrar[m + n0 + 1].key, adr]

User applied rule all left

And obtained the following new goals

Proof step 19:
m < # zbrar, m + nused0 < # zbrar, n0 < nused0, sorted(zbrar, m, nused0 + 1), n0 < nused0 ∧ sorted(zbrar, m + 1, nused0) ∧ (m + 1) + nused0 ≤ # zbrar → 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] ⊦ (zbrar[m].entry? ⊃ payload(zbrar[m + n0 + 1, mkzentry(zbrar[m + n0 + 1].key, adr)], m + 1, nused0)[zbrar[m].key, zbrar[m].adr] ;payload(zbrar[m + n0 + 1, mkzentry(zbrar[m + n0 + 1].key, adr)], m + 1, nused0) ) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0))[zbrar[m + n0 + 1].key, adr]

Rule argument

pos: left 5 terms: n0, zbrar, m + 1, adr abort: F discard: T computed: F

Additional information

Used terms: n0, zbrar, m + 1, adr