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Proof step 26 from proof getarray-offset (previous step)

1 < j - j0, j0 ≤ j, 1 < j, 0 < j, 0 ≤ j0, 0 ≤ j, ∀ j1, j0, r, i, st. i→n(j1) < i→n(j) → (j0 ≤ j1 ∧ 0 ≤ j0 → getarray(r, i, j1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j1 - j0, st)) ⊦ getarray(r, i, j - 1, st) + st[r -- (i + j - 1) '] ' = getarray(r, i, j0, st) + (getarray(r, i + j0, j - j0 - 1, st) + st[r -- ((i + j0) + (j - j0) - 1) '])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
j0 ≤ j, 1 < j, 0 < j, 0 ≤ j0, 0 ≤ j, 1 + j0 < j, ∀ j1, j0, r, i, st. i→n(j1) < i→n(j) → (j0 ≤ j1 ∧ 0 ≤ j0 → getarray(r, i, j1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j1 - j0, st)) ⊦ getarray(r, i, j - 1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j - j0 + 1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ vals + vals0 = vals1 + vals0 ↔ vals = vals1], [CSIMPSEQ : ⊦ vals + val = vals + val '], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i - j - i0 = i - j + i0], [CSIMPSEQ : ⊦ i + j = j + i])]]