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Proof step 20 from proof getarray-in-01 (previous step)

i0 ≤ i, i ≤ i0 + i3, 0 < i3, 0 ≤ i3, ∀ r, st, i, i0, i2. i→n(i2) < i→n(i3 + 1) → (i0 ≤ i ∧ i < i0 + i2 ∧ 0 < i2 → st[r -- i '] ∈ getarray(r, i0, i2, st)) ⊦ st[r -- i '] = st[r -- (i0 + i3) '], st[r -- i '] ∈ getarray(r, i0, i3, st)

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [r, st, i, i0, i2] → [r, st, i, i0, i3]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + 0 = 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, i3)]]