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Proof step 8 from proof get-first (previous step)

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

User applied rule apply induction

And obtained the following new goals

Proof step 7:
getarray(r, i, i0, st) .first = st[r -- i '], 0 < i0, 0 ≤ i0, ∀ j0, r, i, st. i→n(j0) < i→n(i0 + 1) → (0 < j0 → getarray(r, i, j0, st) .first = st[r -- i ']) ⊦ (getarray(r, i, i0, st) + st[r -- (i + i0) '] ') .first = st[r -- i ']

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([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 : (i0, r, i, st)]]