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Proof step 13 from proof comp-same (previous step)

i2 < i1, i + i4 * (i1 - i2) < i3, j0 ≤ i4, 0 ≤ i2, 0 < i1, 0 ≤ j0, 0 ≤ i4, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st[r -- (i1 + j) '] = st[r -- (i2 + j) '], ∀ j, i2, i1, i, i4, i3, st, r. i→n(j) < i→n(j0) → ( i2 < i1 ∧ i + i4 * (i1 - i2) < i3 ∧ 0 ≤ i2 ∧ 0 ≤ i4 ∧ 0 ≤ j ∧ j ≤ i4 ∧ 0 ≤ i ∧ (∀ j. 0 ≤ j ∧ j < i3 → st[r -- (i1 + j) '] = st[r -- (i2 + j) ']) → st[r -- (i1 + i + j * (i1 - i2)) '] = st[r -- (i1 + i) ']) ⊦ st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i1 + i) ']

User applied rule apply induction

And obtained the following new goals

Proof step 2:
i2 < i1, i + i4 * (i1 - i2) < i3, j0 ≤ i4, 0 ≤ i2, 0 < i1, 0 ≤ j0, 0 ≤ i4, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st[r -- (i1 + j) '] = st[r -- (i2 + j) '], ∀ j, i2, i1, i, i4, i3, st, r. i→n(j) < i→n(j0) → ( i2 < i1 ∧ i + i4 * (i1 - i2) < i3 ∧ 0 ≤ i2 ∧ 0 ≤ i4 ∧ 0 ≤ j ∧ j ≤ i4 ∧ 0 ≤ i ∧ (∀ j. 0 ≤ j ∧ j < i3 → st[r -- (i1 + j) '] = st[r -- (i2 + j) ']) → st[r -- (i1 + i + j * (i1 - i2)) '] = st[r -- (i1 + i) ']) ⊦ i2 < i1 ∧ i + i4 * (i1 - i2) < i3 ∧ 0 ≤ i2 ∧ 0 ≤ i4 ∧ 0 ≤ j0 - 1 ∧ j0 - 1 ≤ i4 ∧ 0 ≤ i ∧ (∀ j. 0 ≤ j ∧ j < i3 → st[r -- (i1 + j) '] = st[r -- (i2 + j) ']), st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i1 + i) ']
Proof step 12:
st[r -- (i1 + i + (j0 - 1) * (i1 - i2)) '] = st[r -- (i1 + i) '], i2 < i1, i + i4 * (i1 - i2) < i3, j0 ≤ i4, 0 ≤ i2, 0 < i1, 0 ≤ j0, 0 ≤ i4, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st[r -- (i1 + j) '] = st[r -- (i2 + j) '], ∀ j, i2, i1, i, i4, i3, st, r. i→n(j) < i→n(j0) → ( i2 < i1 ∧ i + i4 * (i1 - i2) < i3 ∧ 0 ≤ i2 ∧ 0 ≤ i4 ∧ 0 ≤ j ∧ j ≤ i4 ∧ 0 ≤ i ∧ (∀ j. 0 ≤ j ∧ j < i3 → st[r -- (i1 + j) '] = st[r -- (i2 + j) ']) → st[r -- (i1 + i + j * (i1 - i2)) '] = st[r -- (i1 + i) ']) ⊦ st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i1 + i) ']

Rule argument

[substlist-arg: [j, i2, i1, i, i4, i3, st, r] → [j0 - 1, i2, i1, i, i4, i3, st, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i * 0 = 0], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRATERMS : (j0 - 1, i2, i1, i, i4, i3, st, r)]]