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Proof step 21 from proof putArray-put (previous step)

0 ≤ j ⊦ (putArray(vals, r, j, st)[r -- (j + n→i(# vals)) ', val]) = putArray(vals + val ', r, j, st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ putArray([], r, i, st) = st
Proof step 2:
⊦ putArray(val ', r, j, st) = st[r -- j ', val]
Proof step 20:
∀ j, r, st, val. 0 ≤ j → (putArray(vals0, r, j, st)[r -- (j + n→i(# vals0)) ', val]) = putArray(vals0 + val ', r, j, st), 0 ≤ j ⊦ (putArray(val0 + vals0, r, j, st)[r -- (j + n→i(# (val0 + vals0))) ', val]) = putArray((val0 + vals0) + val ', r, j, st)

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 : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])]]