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Proof step 10 from proof getarray-addarray-05 (previous step)

j = i0 + 1, 0 ≤ j, 0 ≤ i, i < j, 0 < j, ∀ st, val, r, i, j0. i→n(j0) < i→n(j) → (i ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, 0, i, addarray(r, val, j0, st)) = mklist(val, i→n(i))) ⊦ i = j, getarray(r, 0, i, addarray(r, val, i0, st)[r -- i0 ', val]) = mklist(val, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 ≤ i, i ≤ i0, 0 ≤ i0, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (i ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, 0, i, addarray(r, val, j0, st)) = mklist(val, i→n(i))) ⊦ getarray(r, 0, i, addarray(r, val, i0, st)[r -- i0 ', val]) = mklist(val, i→n(i))

Rule argument

[emptyarg]

Additional information

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