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Proof step 26 from proof payload-mod (previous step)

zbrar[m] = mkzentry(key, adr0), key = zbrar[(m + 1) + n0].key, 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], n0 < nused0, m + nused0 < # zbrar, m < # zbrar, sorted(zbrar, m, nused0 + 1) ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr][key, adr0] = payload(zbrar, m + 1, nused0)[key, adr0][zbrar[m + n0 + 1].key, adr]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
zbrar[m] = mkzentry(zbrar[(m + 1) + n0].key, adr0), 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], m < # zbrar, m + nused0 < # zbrar, n0 < nused0, sorted(zbrar, m, nused0 + 1) ⊦ payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr0] = payload(zbrar, m + 1, nused0)[zbrar[(m + 1) + n0].key, adr]

Rule argument

Additional information

Used simplifier rules: ⊦ ri[key, adr][key, adr0] = ri[key, adr0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic