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Proof step 6 from proof in-1dim-other-index-01 (previous step)

0 ≤ i0, r -- i ' ∈ addarray(r, val, i0, st), r ∈ addarray(r, val, i0, st), i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (true → (i < 0 ∨ j0 ≤ i → (r -- i ' ∈ addarray(r, val, j0, st) ↔ r -- i ' ∈ st))) ⊦ i = i0, r -- i ' ∈ st

User applied rule apply induction

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, val, i, st)

Rule argument

[substlist-arg: [st, val, r, i, j0] → [st, val, r, i, i0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, val, r, i, i0)]]