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Proof step 26 from proof switch-array (previous step)

# vals = m + 1, ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < m + 1 → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ vals = [], r = r0, (addarray(r, ty, vals .butlast, addarray(r0, ty0, vals0, st))[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)]) = addarray(r0, ty0, vals0, addarray(r, ty, vals, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ vals ≠ [] → addarray(r, ty, vals, st) = (addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])
Proof step 25:
vals ≠ [], # vals = m + 1, ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < m + 1 → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ vals = [], r = r0, (addarray(r, ty, vals .butlast, addarray(r0, ty0, vals0, st))[r -- n→i(m) ', vals .last][r -- _length, intval(n→i(m) + 1)]) = addarray(r0, ty0, vals0, addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])

Rule argument

[crewrite-arg: add-lastrec, F, [st, vals, ty, r] → [st, vals, ty, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals, ty, r)]]