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Proof step 8 from proof putArray-put-switch (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ putArray([], r, i, st) = st
Proof step 7:
∀ i, j, r, st, val. i + n→i(# vals0) ≤ j ∧ 0 ≤ j ∧ 0 ≤ i → putArray(vals0, r, i, st[r -- j ', val]) = (putArray(vals0, r, i, st)[r -- j ', val]), i + n→i(# (val0 + vals0)) ≤ j, 0 ≤ j, 0 ≤ i ⊦ putArray(val0 + vals0, r, i, st[r -- j ', val]) = (putArray(val0 + vals0, r, i, st)[r -- j ', val])

Rule argument

[VARWITHVARSEQSARG : vals, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : javavalues generated by [], +;])]]