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Proof step 5 from proof switch-addarray-addobj-01 (previous step)

i1 ≤ 0, ∀ i, st, fis, class, ty, r0, r, i0. i→n(i0) < i→n(i1) → ( true → r = r0 ∨ addarray(r, initial_value(ty), i0, addobj(r0, class, fis, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) = addobj(r0, class, fis, addarray(r, initial_value(ty), i0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]))) ⊦ r0 = r, (addobj(r0, class, fis, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) = (addobj(r0, class, fis, st[r -- _type, typeval(mkarraytype(ty))])[r -- _length, intval(i)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → addobj(r, class1, fis, st[r0 -- sk, val]) = (addobj(r, class1, fis, st)[r0 -- sk, val])

Rule argument

[speclemmaarg: , r ≠ r0 → addobj(r, class1, fis, st[r0 -- sk, val]) = (addobj(r, class1, fis, st)[r0 -- sk, val]) ,[val, sk, r0, st, fis, class1, r] → [typeval(mkarraytype(ty)), _type, r, st, fis, class, r0] ,F ,addfuns , ,addobj-put-switch ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (typeval(mkarraytype(ty)), _type, r, st, fis, class, r0)]]