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Proof step 5 from proof comp-same (previous step)

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) ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ (i + i0) * j = i * j + i0 * j

Rule argument

[speclemmaarg: ,(i + i0) * j = i * j + i0 * j ,[j, i0, i] → [i1 - i2, 1, i0] ,F ,int-mult , ,dist-lsplit ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ 1 * i = i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + i = 2 * i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0])], [EXTRATERMS : (i1 - i2, 1, i0)]]