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Proof step 14 from proof switch-array (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ addarray(r, ty, vals, st) = addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])
Proof step 13:
∀ st, vals0, ty0, ty, r0, r, vals1. # vals1 < # [] → (true → r = r0 ∨ addarray(r, ty, vals1, addarray(r0, ty0, vals0, st)) = addarray(r0, ty0, vals0, addarray(r, ty, vals1, st))) ⊦ addarray(r, [], 0, addarray(r0, ty0, vals0, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# []))]) = addarray(r0, ty0, vals0, addarray(r, ty, [], st)), r = r0

Rule argument

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

Additional information

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