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Proof step 30 from proof switch-array (previous step)

∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < # vals → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ addarray(r, ty, vals, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals, st)), r = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 15:
¬ vals ≠ [], ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < # vals → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ addarray(r, ty, vals, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals, st)), r = r0
Proof step 29:
vals ≠ [], ∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < # vals → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ (addarray(r, ty, vals .butlast, addarray(r0, ty0, vals0, st))[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))]) = addarray(r0, ty0, vals0, addarray(r, ty, vals, st)), r = r0

Rule argument

[crewrite-arg: add-lastrec , F , [st, vals, ty, r] → [addarray(r0, ty0, vals0, st), vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r0, ty0, vals0, st), vals, ty, r)]]