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Proof step 10 from proof getarray-addarray-06 (previous step)

0 ≤ (addarray(r, ty, i, st)[r -- _length]) .intval, 0 ≤ i ⊦ i→n((addarray(r, ty, i, st)[r -- _length]) .intval) = i→n(i) ∧ (n < i→n((addarray(r, ty, i, st)[r -- _length]) .intval) → (addarray(r, ty, i, st)[r -- n→i(n) ']) = (mklist(initial_value(ty), i→n(i))[n]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)
Proof step 9:
n < i→n(i), 0 < i ⊦ (addarray(r, ty, i, st)[r -- n→i(n) ']) = initial_value(ty), i = 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i→n(i) = 0 ↔ i = 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m < n → (mklist(val, n)[m]) = val], [CSIMPSEQ : ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j)], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ intval(i) .intval = i])]]