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Proof step 13 from proof switch-addarray-addobj-01 (previous step)

addarray(r, initial_value(ty), i2, addobj(r0, class, fis, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) = addobj(r0, class, fis, addarray(r, initial_value(ty), i2, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)])), 0 ≤ i2, ∀ i, st, fis, class, ty, r0, r, i0. i→n(i0) < i→n(i2 + 1) → ( 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), i2, addobj(r0, class, fis, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)]) [r -- i2 ', initial_value(ty) ] ) = addobj (r0, class, fis, addarray(r, initial_value(ty), i2, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(i)])[r -- i2 ', initial_value(ty)]), r = r0

User applied rule insert equation

And obtained the following new goals

Rule argument

[inserteqarg: pos: left 1,F,T,()]

Additional information

[[CONCRETESIMPRULES : ()]]