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Proof step 8 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))) ⊦ r0 = r, (addarray(r0, ty0, vals0, st[r -- _type, typeval(mkarraytype(ty))])[r -- _length, intval(0)]) = addarray(r0, ty0, vals0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(0)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk, val]) = addarray(r, ty, vals, st[r0 -- sk, val])

Rule argument

[crewrite-arg: shift-1init , F , [val, sk, r0, st, vals, ty, r] → [intval(0), _length, r, st[r -- _type, typeval(mkarraytype(ty))], vals0, ty0, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (intval(0), _length, r, st[r -- _type, typeval(mkarraytype(ty))], vals0, ty0, r0)]]