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

∀ zbrar, m. save(zbrar, m + 1, nused0)[m, save(zbrar[m])] = save(zbrar, m, nused0)[m + nused0, save(zbrar[m + nused0])] ⊦ save(zbrar, 2 + m, nused0)[m + 1, save(zbrar[m + 1])][m, save(zbrar[m])] = save(zbrar, m + 1, nused0)[m, save(zbrar[m])][m + nused0 + 1, save(zbrar[m + nused0 + 1])]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
m ≠ n ⊦ brar[m, br][n, br0] = brar[n, br0][m, br]
Proof step 13:
∀ zbrar, m. save(zbrar, m + 1, nused0)[m, save(zbrar[m])] = save(zbrar, m, nused0)[m + nused0, save(zbrar[m + nused0])] ⊦ save(zbrar, 2 + m, nused0)[m + 1, save(zbrar[m + 1])][m, save(zbrar[m])] = save(zbrar, m + 1, nused0)[m + nused0 + 1, save(zbrar[m + nused0 + 1])][m, save(zbrar[m])], m = m + nused0 + 1

Rule argument

spec: array, inst: branch-array name: cputput-reverse seq: m ≠ n ⊦ brar[m, br][n, br0] = brar[n, br0][m, br] subst: [br0, n, br, m, brar] → [save(zbrar[m + nused0 + 1]), m + nused0 + 1, save(zbrar[m]), m, save(zbrar, 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: save(zbrar[m + nused0 + 1]), m + nused0 + 1, save(zbrar[m]), m, save(zbrar, m + 1, nused0)