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Proof step 8 from proof getarray-put-01 (previous step)

0 ≤ i1, i + i1 < i0 ∨ i0 < i, ∀ j0, i0, i, r, st, val. i→n(j0) < i→n(i1 + 1) → (i0 < i ∨ i + j0 ≤ i0 → getarray(r, i, j0, st[r -- i0 ', val]) = getarray(r, i, j0, st)) ⊦ ((i = i0 ⊃ val; st[r -- i '])) ' + getarray(r, i + 1, i1, st[r -- i0 ', val]) = getarray(r, i, i1 + 1, st)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 7:
i ≠ i0, 0 ≤ i1, i + i1 < i0 ∨ i0 < i, ∀ j0, i0, i, r, st, val. i→n(j0) < i→n(i1 + 1) → (i0 < i ∨ i + j0 ≤ i0 → getarray(r, i, j0, st[r -- i0 ', val]) = getarray(r, i, j0, st)) ⊦ st[r -- i '] ' + getarray(r, i + 1, i1, st[r -- i0 ', val]) = getarray(r, i, i1 + 1, st)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i < i])]]