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Proof step 9 from proof unmodified-same-payload (previous step)

# zbrar0 = BRANCH_SIZE, BRANCH_SIZE = # zbrar1, iast[adr] = indexnode(save(zbrar0, 0, nused), bv, nused), save(zbrar1, 0, nused) = save(zbrar0, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE ⊦ payload(zbrar0, 0, nused) = payload(zbrar1, 0, nused)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ # zbrar0 = # zbrar1 ∧ n + m ≤ # zbrar0 ∧ # zbrar0 = BRANCH_SIZE ∧ save(zbrar0, n, m) = save(zbrar1, n, m) → payload(zbrar0, n, m) = payload(zbrar1, n, m)

Rule argument

spec: <toplevel> name: save-same-payload-same seq: ⊦ # zbrar0 = # zbrar1 ∧ n + m ≤ # zbrar0 ∧ # zbrar0 = BRANCH_SIZE ∧ save(zbrar0, n, m) = save(zbrar1, n, m) → payload(zbrar0, n, m) = payload(zbrar1, n, m) subst: [zbrar1, m, n, zbrar0] → [zbrar0, nused, 0, zbrar1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: zbrar0, nused, 0, zbrar1