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Proof step 15 from proof payload-split (previous step)

zbrar[m] = mkzentry(key, adr), payload(zbrar, m + 1, n0 + n1) = payload(zbrar, m + 1, n1) ⊕ payload(zbrar, (m + 1) + n1, n0), m + n0 + n1 < # zbrar, m < # zbrar ⊦ # zbrar = 0, payload(zbrar, m + 1, n1 + n0)[key, adr] = payload(zbrar, m + 1, n1)[key, adr] ⊕ payload(zbrar, m + n1 + 1, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: oplus-shift-put-l seq: ⊦ ri[key, adr] ⊕ ri0 = (ri ⊕ ri0)[key, adr] subst: [ri0, adr, key, ri] → [payload(zbrar, m + n1 + 1, n0), adr, key, payload(zbrar, m + 1, n1)] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: payload(zbrar, m + n1 + 1, n0), adr, key, payload(zbrar, m + 1, n1)