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Proof step 16 from proof switch-addarray-addobj-01 (previous step)

i1 = i2 + 1, 0 < i1, ∀ 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), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0])]]