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Proof step 10 from proof at=get (previous step)

i ≤ i0, 0 ≤ i, 0 ≤ i0, 0 < i0, i < i0, ∀ r, st, i, j0. i→n(j0) < i→n(i0 + 1) → (true → (0 ≤ i ∧ i < j0 → st[r -- i '] = (getarray(r, 0, j0, st)[i→n(i)]))) ⊦ st[r -- i '] = (getarray(r, 0, i0, st)[i→n(i)])

User applied rule apply induction

And closed the goal!

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [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 : (r, st, i, i0)]]