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Proof step 22 from proof get-rest (previous step)

getarray(r, i, 1 + i2, st) + st[r -- (1 + i + i2) '] ' = val ' + vals, 0 ≤ i2, 0 < i2, ∀ i1, r, i, st. i→n(i1) < i→n(i2 + 1) → (0 ≤ i1 → getarray(r, i, i1 + 1, st) .rest = getarray(r, i + 1, i1, st)) ⊦ vals = getarray(r, i + 1, i2, st) + st[r -- (i + i2 + 1) '] ', ¬ st[r -- (1 + i + i2) '] ∈ vals ∧ st[r -- (1 + i + i2) '] ≠ val, val ≠ st[r -- (1 + i + i2) '] ∧ ¬ val ∈ getarray(r, i, 1 + i2, st)

User applied rule apply induction

And obtained the following new goals

Proof step 21:
getarray(r, i, i2 + 1, st) .rest = getarray(r, i + 1, i2, st), getarray(r, i, 1 + i2, st) + st[r -- (1 + i + i2) '] ' = val ' + vals, 0 ≤ i2, 0 < i2, ∀ i1, r, i, st. i→n(i1) < i→n(i2 + 1) → (0 ≤ i1 → getarray(r, i, i1 + 1, st) .rest = getarray(r, i + 1, i1, st)) ⊦ vals = getarray(r, i + 1, i2, st) + st[r -- (i + i2 + 1) '] ', ¬ st[r -- (1 + i + i2) '] ∈ vals ∧ st[r -- (1 + i + i2) '] ≠ val, val ≠ st[r -- (1 + i + i2) '] ∧ ¬ val ∈ getarray(r, i, 1 + i2, st)

Rule argument

[substlist-arg: [i1, r, i, st] → [i2, 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 : (i2, r, i, st)]]