| ¬ j ≤ 0, 0 ≤ j, 0 ≤ j0, j0 ≤ 1, 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, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j - j0, st) |
⊦ getarray(r, i, 1, st) = st[r -- i '] '
0 ≤ j0, j0 ≤ 1, ∀ j1, j0, r, i, st. i→n(j1) < i→n(1) → (j0 ≤ j1 ∧ 0 ≤ j0 → getarray(r, i, j1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j1 - j0, st)) ⊦ st[r -- i '] ' = getarray(r, i, j0, st) + getarray(r, i + j0, 1 - j0, st)
[[CONCRETESIMPRULES : ([CSIMPSEQ : j0 ≠ 0, j ≤ j0 ⊦ i ≤ ((* j)) → i ≤ ((* j0))], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)])]]