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Proof step 133 from proof addarray-put-01 (previous step)

0 ≤ i ∧ i < n→i(# (val ' + mklist(initial_value(ty), i→n(i0)))), 0 ≤ i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 < i → 0 < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)])]]