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Proof step 3 from proof addarray-mklist (previous step)

0 ≤ j ⊦ addarray(r, mklist(initial_value(byte_type), i→n(j)), 0, st) = addarray(r, initial_value(byte_type), j, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ 0 ≤ i ∧ 0 ≤ j → addarray(r, mklist(initial_value(byte_type), i→n(j)), i, addarray(r, mklist(initial_value(byte_type), i→n(i)), 0, st)) = addarray(r, initial_value(byte_type), j + i, st)
Proof step 2:
⊦ addarray(r, [], i, st) = st

Rule argument

[LEMMAARG : addarray-mklist-01, [i, j, r, st] → [0, j, r, st]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ mklist(val, 0) = []], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (0, j, r, st)]]