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Proof step 6 from proof comp-same (previous step)

j0 = i0 + 1, st[r -- (i1 + i + j0 * (i1 - i2)) '] = st[r -- (i2 + i + j0 * (i1 - i2)) '], st[r -- (i1 + i + i0 * (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 -- (i2 + i + j0 * (i1 - i2)) '] = st[r -- (i1 + i) '], i2 + j0 * (i1 - i2) = i1 + i0 * (i1 - i2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
st[r -- (i1 + i + i0 * (i1 - i2)) '] = st[r -- (i1 + i) '], st[r -- (i1 + i + (i0 + 1) * (i1 - i2)) '] = st[r -- (i2 + i + (i0 + 1) * (i1 - i2)) '], (~1) ≤ i0, 0 < i1, 0 ≤ i2, i0 < i4, i + i4 * (i1 - i2) < i3, i2 < i1, 0 ≤ i, 0 ≤ i4, ∀ 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(i0 + 1) → ( 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 + (i0 + 1) * (i1 - i2) = i1 + i0 * (i1 - i2), st[r -- (i2 + i + (i0 + 1) * (i1 - i2)) '] = st[r -- (i1 + i) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j])]]