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Proof step 126 from proof addarray-put-01 (previous step)

i→n(i) = m + 1, 0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (mklist(initial_value(ty), i→n(i0))[m])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)
Proof step 125:
0 ≤ i ∧ i < 1 + i0, i→n(i) = m + 1, 0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i0))[m])

Rule argument

[crewrite-arg: at-1dim, F, [j, st, i, ty, r] → [i, st, 1 + i0, ty, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (i, st, 1 + i0, ty, r)]]