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Proof step 11 from proof load-branches-last (previous step)

∀ brar, m. load(brar, m + 1, nused0)[m, load(brar[m])] = load(brar, m, nused0)[m + nused0, load(brar[m + nused0])] ⊦ load(brar, 2 + m, nused0)[m + 1, load(brar[m + 1])][m, load(brar[m])] = load(brar, m + 1, nused0)[m, load(brar[m])][m + nused0 + 1, load(brar[m + nused0 + 1])]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
m ≠ n ⊦ zbrar[m, zbr][n, zbr0] = zbrar[n, zbr0][m, zbr]
Proof step 13:
∀ brar, m. load(brar, m + 1, nused0)[m, load(brar[m])] = load(brar, m, nused0)[m + nused0, load(brar[m + nused0])] ⊦ load(brar, 2 + m, nused0)[m + 1, load(brar[m + 1])][m, load(brar[m])] = load(brar, m + 1, nused0)[m + nused0 + 1, load(brar[m + nused0 + 1])][m, load(brar[m])], m = m + nused0 + 1

Rule argument

spec: array, inst: zbranch-array name: cputput-reverse seq: m ≠ n ⊦ zbrar[m, zbr][n, zbr0] = zbrar[n, zbr0][m, zbr] subst: [zbr0, n, zbr, m, zbrar] → [load(brar[m + nused0 + 1]), m + nused0 + 1, load(brar[m]), m, load(brar, m + 1, nused0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m = m + n ↔ n = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: load(brar[m + nused0 + 1]), m + nused0 + 1, load(brar[m]), m, load(brar, m + 1, nused0)