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Proof step 13 from proof payload-mod (previous step)

m < # zbrar, m + nused0 < # 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] ⊦ payload(zbrar, m + 1, nused0)[zbrar[m].key, adr] = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0))[zbrar[m].key, adr]

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ri[key, adr][key, adr0] = ri[key, adr0]; (s)