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Proof step 179 from proof addarray-put-01 (previous step)

¬ i→n(i) < # mklist(initial_value(ty), i→n(j)), 0 ≤ i0, 0 ≤ i0 + j, 0 < j, i ≤ i0 + j, 0 ≤ i, i ≤ j + i0 ⊦ j = 0, initial_value(ty) = (mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 178:
1 < i0 + j, 1 < i, 0 < i, j < i, i ≤ j + i0, 0 ≤ i, i ≤ i0 + j, 0 < j, 0 ≤ i0 + j, 0 ≤ i0, 0 < i0 ⊦ initial_value(ty) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i) - i→n(j)], j = 0, i = j

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 < i ∧ 0 < j → 0 < i + j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 < i → 0 < j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPFORWARD : ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 < j → abs(j) = j], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]])]]