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Proof step 4 from proof getarray-put-01 (previous step)

0 ≤ i1, i + i1 < i0 ∨ i0 < i, ∀ j0, i0, i, r, st, val. i→n(j0) < i→n(i1 + 1) → (i0 < i ∨ i + j0 ≤ i0 → getarray(r, i, j0, st[r -- i0 ', val]) = getarray(r, i, j0, st)) ⊦ i = i0, getarray(r, i + 1, i1, st[r -- i0 ', val]) = getarray(r, i + 1, i1, st)

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [j0, i0, i, r, st, val] → [i1, i0, i + 1, r, st, val]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [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 : (i1, i0, i + 1, r, st, val)]]