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Proof step 2 from proof in-1dim-15 (previous step)

0 ≤ j, j < i1, 0 < i1, 0 ≤ i1, ∀ st, val, r, j, i0. i→n(i0) < i→n(i1 + 1) → (j < i0 ∧ 0 ≤ j ∧ 0 < i0 → r -- j ' ∈ addarray(r, val, i0, st)) ⊦ i1 = j, r -- j ' ∈ addarray(r, val, i1, st)

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [st, val, r, j, i0] → [st, val, r, j, i1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [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 < j → abs(j) = j], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, val, r, j, i1)]]