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Proof step 11 from proof init-at-01 (conclusion)

⊦ j ≤ i ∧ i < j + n→i(# vals) → (addarray(r, vals, j, st)[r -- i ']) = vals[i→n(i - j)]

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ addarray(r, [], i, st) = st
Proof step 10:
∀ j, i, r, st. j ≤ i ∧ i < j + n→i(# vals0) → (addarray(r, vals0, j, st)[r -- i ']) = vals0[i→n(i - j)] ⊦ j ≤ i ∧ i < j + n→i(# (val + vals0)) → (addarray(r, val + vals0, j, st)[r -- i ']) = (val + vals0)[i→n(i - j)]

Rule argument

[VARWITHVARSEQSARG : vals, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : javavalues generated by [], +;], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]