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Proof step 229 from proof putarray-addarray-01 (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j → putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray (r, ty, mklist(initial_value(ty), i→n(i)) + vals + ((j - i + n→i(# vals) > 0 ⊃ mklist(initial_value(ty), i→n(j - i + n→i(# vals))); [])), st) [r -- _length, intval(j) ] )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 228:
i ≤ j, 0 ≤ i, 0 ≤ j ⊦ putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + ((¬ j ≤ n→i(# vals) + i ⊃ mklist(initial_value(ty), i→n(j - i + n→i(# vals))); [])), st) [r -- _length, intval(j) ] )

Rule argument

[emptyarg]

Additional information

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