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Proof step 6 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, m + 1, nused0 + 1)[m, load(brar[m])] = load(brar, m, nused0 + 1)[m + nused0 + 1, load(brar[m + nused0 + 1])]

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used terms: nused0, m + 1, brar