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Proof step 11 from proof comp-same (previous step)

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, ¬ i + j0 * (i1 - i2) < 0 ∧ ¬ i3 ≤ i + j0 * (i1 - i2) → st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i2 + i + j0 * (i1 - i2)) '], ∀ 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 case distinction

And obtained the following new goals

Proof step 10:
st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i2 + i + j0 * (i1 - i2)) '], 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

[CASEDARG : pos: left 10, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPSEQ : ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬ (j < 0 ∧ i ≠ 0))], [CSIMPSEQ : ⊦ i - j < i0 ↔ i < j + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i0 < i → ( (i - i0) * j < (i - i0) * j0 ↔ j < j0)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]