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Proof step 19 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)]))) ⊦ (addarray(r, initial_value(ty), i1 - 1, addobj(r0, class, fis, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) [r -- (i1 - 1) ', initial_value(ty) ] ) = addobj(r0, class, fis, addarray(r, initial_value(ty), i1, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)])), r = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[crewrite-arg: addarray-rec , F , [st, i, val, r] → [st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)], i1, initial_value(ty), r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(i) ], i1, initial_value(ty), r)]]