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Proof step 6 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, m + 1, nused0 + 1)[m, save(zbrar[m])] = save(zbrar, m, nused0 + 1)[m + nused0 + 1, save(zbrar[m + nused0 + 1])]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ save(zbrar, m, nused + 1) = save(zbrar, m + 1, nused)[m, save(zbrar[m])]
Proof step 8:
∀ zbrar, m. save(zbrar, m + 1, nused0)[m, save(zbrar[m])] = save(zbrar, m, nused0)[m + nused0, save(zbrar[m + nused0])] ⊦ save(zbrar, (m + 1) + 1, nused0)[m + 1, save(zbrar[m + 1])][m, save(zbrar[m])] = save(zbrar, m, nused0 + 1)[m + nused0 + 1, save(zbrar[m + nused0 + 1])]

Rule argument

spec: <toplevel> name: save-branches-rec seq: ⊦ save(zbrar, m, nused + 1) = save(zbrar, m + 1, nused)[m, save(zbrar[m])] subst: [nused, m, zbrar] → [nused0, m + 1, zbrar] flags: <all paths>

Additional information

Used terms: nused0, m + 1, zbrar